diff --git a/src/material-experimental/mdc-menu/menu.spec.ts b/src/material-experimental/mdc-menu/menu.spec.ts
index 36023c0fb6b0..09e6b24cfba0 100644
--- a/src/material-experimental/mdc-menu/menu.spec.ts
+++ b/src/material-experimental/mdc-menu/menu.spec.ts
@@ -89,6 +89,19 @@ describe('MDC-based MatMenu', () => {
     );
   }));
 
+  it('should set aria-haspopup based on whether a menu is assigned', fakeAsync(() => {
+    const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
+    fixture.detectChanges();
+    const triggerElement = fixture.componentInstance.triggerEl.nativeElement;
+
+    expect(triggerElement.getAttribute('aria-haspopup')).toBe('true');
+
+    fixture.componentInstance.trigger.menu = null;
+    fixture.detectChanges();
+
+    expect(triggerElement.hasAttribute('aria-haspopup')).toBe(false);
+  }));
+
   it('should open the menu as an idempotent operation', fakeAsync(() => {
     const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
     fixture.detectChanges();
@@ -828,20 +841,6 @@ describe('MDC-based MatMenu', () => {
     expect(triggerEl.hasAttribute('aria-expanded')).toBe(false);
   }));
 
-  it('should throw the correct error if the menu is not defined after init', fakeAsync(() => {
-    const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
-    fixture.detectChanges();
-
-    fixture.componentInstance.trigger.menu = null!;
-    fixture.detectChanges();
-
-    expect(() => {
-      fixture.componentInstance.trigger.openMenu();
-      fixture.detectChanges();
-      tick(500);
-    }).toThrowError(/must pass in an mat-menu instance/);
-  }));
-
   it('should throw if assigning a menu that contains the trigger', fakeAsync(() => {
     expect(() => {
       const fixture = createComponent(InvalidRecursiveMenu, [], [FakeIcon]);
diff --git a/src/material/menu/menu-errors.ts b/src/material/menu/menu-errors.ts
index 16a855a38e75..6027d4e3da5d 100644
--- a/src/material/menu/menu-errors.ts
+++ b/src/material/menu/menu-errors.ts
@@ -6,18 +6,6 @@
  * found in the LICENSE file at https://angular.io/license
  */
 
-/**
- * Throws an exception for the case when menu trigger doesn't have a valid mat-menu instance
- * @docs-private
- */
-export function throwMatMenuMissingError() {
-  throw Error(`matMenuTriggerFor: must pass in an mat-menu instance.
-
-    Example:
-      <mat-menu #menu="matMenu"></mat-menu>
-      <button [matMenuTriggerFor]="menu"></button>`);
-}
-
 /**
  * Throws an exception for the case when menu's x-position value isn't valid.
  * In other words, it doesn't match 'before' or 'after'.
diff --git a/src/material/menu/menu-trigger.ts b/src/material/menu/menu-trigger.ts
index ff1b4c208f20..fcfdbf44a325 100644
--- a/src/material/menu/menu-trigger.ts
+++ b/src/material/menu/menu-trigger.ts
@@ -43,7 +43,7 @@ import {normalizePassiveListenerOptions} from '@angular/cdk/platform';
 import {asapScheduler, merge, Observable, of as observableOf, Subscription} from 'rxjs';
 import {delay, filter, take, takeUntil} from 'rxjs/operators';
 import {_MatMenuBase, MenuCloseReason} from './menu';
-import {throwMatMenuMissingError, throwMatMenuRecursiveError} from './menu-errors';
+import {throwMatMenuRecursiveError} from './menu-errors';
 import {MatMenuItem} from './menu-item';
 import {MAT_MENU_PANEL, MatMenuPanel} from './menu-panel';
 import {MenuPositionX, MenuPositionY} from './menu-positions';
@@ -75,7 +75,7 @@ const passiveEventListenerOptions = normalizePassiveListenerOptions({passive: tr
 
 @Directive({
   host: {
-    'aria-haspopup': 'true',
+    '[attr.aria-haspopup]': 'menu ? true : null',
     '[attr.aria-expanded]': 'menuOpen || null',
     '[attr.aria-controls]': 'menuOpen ? menu.panelId : null',
     '(click)': '_handleClick($event)',
@@ -117,19 +117,19 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
    * @breaking-change 8.0.0
    */
   @Input('mat-menu-trigger-for')
-  get _deprecatedMatMenuTriggerFor(): MatMenuPanel {
+  get _deprecatedMatMenuTriggerFor(): MatMenuPanel | null {
     return this.menu;
   }
-  set _deprecatedMatMenuTriggerFor(v: MatMenuPanel) {
+  set _deprecatedMatMenuTriggerFor(v: MatMenuPanel | null) {
     this.menu = v;
   }
 
   /** References the menu instance that the trigger is associated with. */
   @Input('matMenuTriggerFor')
-  get menu() {
+  get menu(): MatMenuPanel | null {
     return this._menu;
   }
-  set menu(menu: MatMenuPanel) {
+  set menu(menu: MatMenuPanel | null) {
     if (menu === this._menu) {
       return;
     }
@@ -152,7 +152,7 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
       });
     }
   }
-  private _menu: MatMenuPanel;
+  private _menu: MatMenuPanel | null;
 
   /** Data to be passed along to any lazily-rendered content. */
   @Input('matMenuTriggerData') menuData: any;
@@ -244,7 +244,6 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
   }
 
   ngAfterContentInit() {
-    this._checkMenu();
     this._handleHover();
   }
 
@@ -287,31 +286,31 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
 
   /** Opens the menu. */
   openMenu(): void {
-    if (this._menuOpen) {
+    const menu = this.menu;
+
+    if (this._menuOpen || !menu) {
       return;
     }
 
-    this._checkMenu();
-
-    const overlayRef = this._createOverlay();
+    const overlayRef = this._createOverlay(menu);
     const overlayConfig = overlayRef.getConfig();
     const positionStrategy = overlayConfig.positionStrategy as FlexibleConnectedPositionStrategy;
 
-    this._setPosition(positionStrategy);
+    this._setPosition(menu, positionStrategy);
     overlayConfig.hasBackdrop =
-      this.menu.hasBackdrop == null ? !this.triggersSubmenu() : this.menu.hasBackdrop;
-    overlayRef.attach(this._getPortal());
+      menu.hasBackdrop == null ? !this.triggersSubmenu() : menu.hasBackdrop;
+    overlayRef.attach(this._getPortal(menu));
 
-    if (this.menu.lazyContent) {
-      this.menu.lazyContent.attach(this.menuData);
+    if (menu.lazyContent) {
+      menu.lazyContent.attach(this.menuData);
     }
 
     this._closingActionsSubscription = this._menuClosingActions().subscribe(() => this.closeMenu());
-    this._initMenu();
+    this._initMenu(menu);
 
-    if (this.menu instanceof _MatMenuBase) {
-      this.menu._startAnimation();
-      this.menu._directDescendantItems.changes.pipe(takeUntil(this.menu.close)).subscribe(() => {
+    if (menu instanceof _MatMenuBase) {
+      menu._startAnimation();
+      menu._directDescendantItems.changes.pipe(takeUntil(menu.close)).subscribe(() => {
         // Re-adjust the position without locking when the amount of items
         // changes so that the overlay is allowed to pick a new optimal position.
         positionStrategy.withLockedPosition(false).reapplyLastPosition();
@@ -322,7 +321,7 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
 
   /** Closes the menu. */
   closeMenu(): void {
-    this.menu.close.emit();
+    this.menu?.close.emit();
   }
 
   /**
@@ -386,10 +385,7 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
       }
     } else {
       this._setIsMenuOpen(false);
-
-      if (menu.lazyContent) {
-        menu.lazyContent.detach();
-      }
+      menu?.lazyContent?.detach();
     }
   }
 
@@ -397,26 +393,26 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
    * This method sets the menu state to open and focuses the first item if
    * the menu was opened via the keyboard.
    */
-  private _initMenu(): void {
-    this.menu.parentMenu = this.triggersSubmenu() ? this._parentMaterialMenu : undefined;
-    this.menu.direction = this.dir;
-    this._setMenuElevation();
-    this.menu.focusFirstItem(this._openedBy || 'program');
+  private _initMenu(menu: MatMenuPanel): void {
+    menu.parentMenu = this.triggersSubmenu() ? this._parentMaterialMenu : undefined;
+    menu.direction = this.dir;
+    this._setMenuElevation(menu);
+    menu.focusFirstItem(this._openedBy || 'program');
     this._setIsMenuOpen(true);
   }
 
   /** Updates the menu elevation based on the amount of parent menus that it has. */
-  private _setMenuElevation(): void {
-    if (this.menu.setElevation) {
+  private _setMenuElevation(menu: MatMenuPanel): void {
+    if (menu.setElevation) {
       let depth = 0;
-      let parentMenu = this.menu.parentMenu;
+      let parentMenu = menu.parentMenu;
 
       while (parentMenu) {
         depth++;
         parentMenu = parentMenu.parentMenu;
       }
 
-      this.menu.setElevation(depth);
+      menu.setElevation(depth);
     }
   }
 
@@ -430,24 +426,17 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
     }
   }
 
-  /**
-   * This method checks that a valid instance of MatMenu has been passed into
-   * matMenuTriggerFor. If not, an exception is thrown.
-   */
-  private _checkMenu() {
-    if (!this.menu && (typeof ngDevMode === 'undefined' || ngDevMode)) {
-      throwMatMenuMissingError();
-    }
-  }
-
   /**
    * This method creates the overlay from the provided menu's template and saves its
    * OverlayRef so that it can be attached to the DOM when openMenu is called.
    */
-  private _createOverlay(): OverlayRef {
+  private _createOverlay(menu: MatMenuPanel): OverlayRef {
     if (!this._overlayRef) {
-      const config = this._getOverlayConfig();
-      this._subscribeToPositions(config.positionStrategy as FlexibleConnectedPositionStrategy);
+      const config = this._getOverlayConfig(menu);
+      this._subscribeToPositions(
+        menu,
+        config.positionStrategy as FlexibleConnectedPositionStrategy,
+      );
       this._overlayRef = this._overlay.create(config);
 
       // Consume the `keydownEvents` in order to prevent them from going to another overlay.
@@ -463,7 +452,7 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
    * This method builds the configuration object needed to create the overlay, the OverlayState.
    * @returns OverlayConfig
    */
-  private _getOverlayConfig(): OverlayConfig {
+  private _getOverlayConfig(menu: MatMenuPanel): OverlayConfig {
     return new OverlayConfig({
       positionStrategy: this._overlay
         .position()
@@ -471,8 +460,8 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
         .withLockedPosition()
         .withGrowAfterOpen()
         .withTransformOriginOn('.mat-menu-panel, .mat-mdc-menu-panel'),
-      backdropClass: this.menu.backdropClass || 'cdk-overlay-transparent-backdrop',
-      panelClass: this.menu.overlayPanelClass,
+      backdropClass: menu.backdropClass || 'cdk-overlay-transparent-backdrop',
+      panelClass: menu.overlayPanelClass,
       scrollStrategy: this._scrollStrategy(),
       direction: this._dir,
     });
@@ -483,8 +472,8 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
    * on the menu based on the new position. This ensures the animation origin is always
    * correct, even if a fallback position is used for the overlay.
    */
-  private _subscribeToPositions(position: FlexibleConnectedPositionStrategy): void {
-    if (this.menu.setPositionClasses) {
+  private _subscribeToPositions(menu: MatMenuPanel, position: FlexibleConnectedPositionStrategy) {
+    if (menu.setPositionClasses) {
       position.positionChanges.subscribe(change => {
         const posX: MenuPositionX = change.connectionPair.overlayX === 'start' ? 'after' : 'before';
         const posY: MenuPositionY = change.connectionPair.overlayY === 'top' ? 'below' : 'above';
@@ -493,9 +482,9 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
         // `positionChanges` fires outside of the `ngZone` and `setPositionClasses` might be
         // updating something in the view so we need to bring it back in.
         if (this._ngZone) {
-          this._ngZone.run(() => this.menu.setPositionClasses!(posX, posY));
+          this._ngZone.run(() => menu.setPositionClasses!(posX, posY));
         } else {
-          this.menu.setPositionClasses!(posX, posY);
+          menu.setPositionClasses!(posX, posY);
         }
       });
     }
@@ -506,12 +495,12 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
    * so the overlay connects with the trigger correctly.
    * @param positionStrategy Strategy whose position to update.
    */
-  private _setPosition(positionStrategy: FlexibleConnectedPositionStrategy) {
+  private _setPosition(menu: MatMenuPanel, positionStrategy: FlexibleConnectedPositionStrategy) {
     let [originX, originFallbackX]: HorizontalConnectionPos[] =
-      this.menu.xPosition === 'before' ? ['end', 'start'] : ['start', 'end'];
+      menu.xPosition === 'before' ? ['end', 'start'] : ['start', 'end'];
 
     let [overlayY, overlayFallbackY]: VerticalConnectionPos[] =
-      this.menu.yPosition === 'above' ? ['bottom', 'top'] : ['top', 'bottom'];
+      menu.yPosition === 'above' ? ['bottom', 'top'] : ['top', 'bottom'];
 
     let [originY, originFallbackY] = [overlayY, overlayFallbackY];
     let [overlayX, overlayFallbackX] = [originX, originFallbackX];
@@ -520,10 +509,10 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
     if (this.triggersSubmenu()) {
       // When the menu is a sub-menu, it should always align itself
       // to the edges of the trigger, instead of overlapping it.
-      overlayFallbackX = originX = this.menu.xPosition === 'before' ? 'start' : 'end';
+      overlayFallbackX = originX = menu.xPosition === 'before' ? 'start' : 'end';
       originFallbackX = overlayX = originX === 'end' ? 'start' : 'end';
       offsetY = overlayY === 'bottom' ? MENU_PANEL_TOP_PADDING : -MENU_PANEL_TOP_PADDING;
-    } else if (!this.menu.overlapTrigger) {
+    } else if (!menu.overlapTrigger) {
       originY = overlayY === 'top' ? 'bottom' : 'top';
       originFallbackY = overlayFallbackY === 'top' ? 'bottom' : 'top';
     }
@@ -644,12 +633,12 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
   }
 
   /** Gets the portal that should be attached to the overlay. */
-  private _getPortal(): TemplatePortal {
+  private _getPortal(menu: MatMenuPanel): TemplatePortal {
     // Note that we can avoid this check by keeping the portal on the menu panel.
     // While it would be cleaner, we'd have to introduce another required method on
     // `MatMenuPanel`, making it harder to consume.
-    if (!this._portal || this._portal.templateRef !== this.menu.templateRef) {
-      this._portal = new TemplatePortal(this.menu.templateRef, this._viewContainerRef);
+    if (!this._portal || this._portal.templateRef !== menu.templateRef) {
+      this._portal = new TemplatePortal(menu.templateRef, this._viewContainerRef);
     }
 
     return this._portal;
diff --git a/src/material/menu/menu.spec.ts b/src/material/menu/menu.spec.ts
index 6fec2b2a6a7b..c54d53601840 100644
--- a/src/material/menu/menu.spec.ts
+++ b/src/material/menu/menu.spec.ts
@@ -89,6 +89,19 @@ describe('MatMenu', () => {
     );
   }));
 
+  it('should set aria-haspopup based on whether a menu is assigned', fakeAsync(() => {
+    const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
+    fixture.detectChanges();
+    const triggerElement = fixture.componentInstance.triggerEl.nativeElement;
+
+    expect(triggerElement.getAttribute('aria-haspopup')).toBe('true');
+
+    fixture.componentInstance.trigger.menu = null;
+    fixture.detectChanges();
+
+    expect(triggerElement.hasAttribute('aria-haspopup')).toBe(false);
+  }));
+
   it('should open the menu as an idempotent operation', fakeAsync(() => {
     const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
     fixture.detectChanges();
@@ -827,20 +840,6 @@ describe('MatMenu', () => {
     expect(triggerEl.hasAttribute('aria-expanded')).toBe(false);
   }));
 
-  it('should throw the correct error if the menu is not defined after init', fakeAsync(() => {
-    const fixture = createComponent(SimpleMenu, [], [FakeIcon]);
-    fixture.detectChanges();
-
-    fixture.componentInstance.trigger.menu = null!;
-    fixture.detectChanges();
-
-    expect(() => {
-      fixture.componentInstance.trigger.openMenu();
-      fixture.detectChanges();
-      tick(500);
-    }).toThrowError(/must pass in an mat-menu instance/);
-  }));
-
   it('should throw if assigning a menu that contains the trigger', fakeAsync(() => {
     expect(() => {
       const fixture = createComponent(InvalidRecursiveMenu, [], [FakeIcon]);
diff --git a/tools/public_api_guard/material/menu.md b/tools/public_api_guard/material/menu.md
index 8b887138a04a..264db2cc79f1 100644
--- a/tools/public_api_guard/material/menu.md
+++ b/tools/public_api_guard/material/menu.md
@@ -287,15 +287,15 @@ export abstract class _MatMenuTriggerBase implements AfterContentInit, OnDestroy
     constructor(overlay: Overlay, element: ElementRef<HTMLElement>, viewContainerRef: ViewContainerRef, scrollStrategy: any, parentMenu: MatMenuPanel, menuItemInstance: MatMenuItem, dir: Directionality, focusMonitor: FocusMonitor);
     closeMenu(): void;
     // @deprecated (undocumented)
-    get _deprecatedMatMenuTriggerFor(): MatMenuPanel;
-    set _deprecatedMatMenuTriggerFor(v: MatMenuPanel);
+    get _deprecatedMatMenuTriggerFor(): MatMenuPanel | null;
+    set _deprecatedMatMenuTriggerFor(v: MatMenuPanel | null);
     get dir(): Direction;
     focus(origin?: FocusOrigin, options?: FocusOptions): void;
     _handleClick(event: MouseEvent): void;
     _handleKeydown(event: KeyboardEvent): void;
     _handleMousedown(event: MouseEvent): void;
-    get menu(): MatMenuPanel;
-    set menu(menu: MatMenuPanel);
+    get menu(): MatMenuPanel | null;
+    set menu(menu: MatMenuPanel | null);
     readonly menuClosed: EventEmitter<void>;
     menuData: any;
     get menuOpen(): boolean;