diff --git a/packages/mui-material/src/Select/Select.test.js b/packages/mui-material/src/Select/Select.test.js
index 273f9f51caf3ad..bb00594406304f 100644
--- a/packages/mui-material/src/Select/Select.test.js
+++ b/packages/mui-material/src/Select/Select.test.js
@@ -11,6 +11,7 @@ import {
 } from 'test/utils';
 import { createTheme, ThemeProvider } from '@mui/material/styles';
 import MenuItem from '@mui/material/MenuItem';
+import ListSubheader from '@mui/material/ListSubheader';
 import InputBase from '@mui/material/InputBase';
 import OutlinedInput from '@mui/material/OutlinedInput';
 import InputLabel from '@mui/material/InputLabel';
@@ -484,6 +485,88 @@ describe('<Select />', () => {
       expect(getAllByRole('option')[1]).to.have.attribute('aria-selected', 'true');
     });
 
+    describe('when the first child is a ListSubheader', () => {
+      it('first selectable option is focused to use the arrow', () => {
+        const { getAllByRole } = render(
+          <Select defaultValue="" open>
+            <ListSubheader>Category 1</ListSubheader>
+            <MenuItem value={1}>Option 1</MenuItem>
+            <MenuItem value={2}>Option 2</MenuItem>
+            <ListSubheader>Category 2</ListSubheader>
+            <MenuItem value={3}>Option 3</MenuItem>
+            <MenuItem value={4}>Option 4</MenuItem>
+          </Select>,
+        );
+
+        const options = getAllByRole('option');
+        expect(options[1]).to.have.attribute('tabindex', '0');
+
+        act(() => {
+          fireEvent.keyDown(options[1], { key: 'ArrowDown' });
+          fireEvent.keyDown(options[2], { key: 'ArrowDown' });
+          fireEvent.keyDown(options[4], { key: 'Enter' });
+        });
+
+        expect(options[4]).to.have.attribute('aria-selected', 'true');
+      });
+
+      describe('when also the second child is a ListSubheader', () => {
+        it('first selectable option is focused to use the arrow', () => {
+          const { getAllByRole } = render(
+            <Select defaultValue="" open>
+              <ListSubheader>Empty category</ListSubheader>
+              <ListSubheader>Category 1</ListSubheader>
+              <MenuItem value={1}>Option 1</MenuItem>
+              <MenuItem value={2}>Option 2</MenuItem>
+              <ListSubheader>Category 2</ListSubheader>
+              <MenuItem value={3}>Option 3</MenuItem>
+              <MenuItem value={4}>Option 4</MenuItem>
+            </Select>,
+          );
+
+          const options = getAllByRole('option');
+          expect(options[2]).to.have.attribute('tabindex', '0');
+
+          act(() => {
+            fireEvent.keyDown(options[2], { key: 'ArrowDown' });
+            fireEvent.keyDown(options[3], { key: 'ArrowDown' });
+            fireEvent.keyDown(options[5], { key: 'Enter' });
+          });
+
+          expect(options[5]).to.have.attribute('aria-selected', 'true');
+        });
+      });
+    });
+
+    describe('when the first child is a MenuItem disabled', () => {
+      it('first selectable option is focused to use the arrow', () => {
+        const { getAllByRole } = render(
+          <Select defaultValue="" open>
+            <MenuItem value="" disabled>
+              <em>None</em>
+            </MenuItem>
+            <ListSubheader>Category 1</ListSubheader>
+            <MenuItem value={1}>Option 1</MenuItem>
+            <MenuItem value={2}>Option 2</MenuItem>
+            <ListSubheader>Category 2</ListSubheader>
+            <MenuItem value={3}>Option 3</MenuItem>
+            <MenuItem value={4}>Option 4</MenuItem>
+          </Select>,
+        );
+
+        const options = getAllByRole('option');
+        expect(options[2]).to.have.attribute('tabindex', '0');
+
+        act(() => {
+          fireEvent.keyDown(options[2], { key: 'ArrowDown' });
+          fireEvent.keyDown(options[3], { key: 'ArrowDown' });
+          fireEvent.keyDown(options[5], { key: 'Enter' });
+        });
+
+        expect(options[5]).to.have.attribute('aria-selected', 'true');
+      });
+    });
+
     it('it will fallback to its content for the accessible name when it has no name', () => {
       const { getByRole } = render(<Select value="" />);
 
diff --git a/packages/mui-material/src/Select/SelectInput.js b/packages/mui-material/src/Select/SelectInput.js
index 1c20c299bb496c..2fb310e5eb26b7 100644
--- a/packages/mui-material/src/Select/SelectInput.js
+++ b/packages/mui-material/src/Select/SelectInput.js
@@ -348,7 +348,7 @@ const SelectInput = React.forwardRef(function SelectInput(props, ref) {
     }
   }
 
-  const items = childrenArray.map((child) => {
+  const items = childrenArray.map((child, index, arr) => {
     if (!React.isValidElement(child)) {
       return null;
     }
@@ -389,6 +389,26 @@ const SelectInput = React.forwardRef(function SelectInput(props, ref) {
       foundMatch = true;
     }
 
+    if (child.props.value === undefined) {
+      return React.cloneElement(child, {
+        'aria-readonly': true,
+        role: 'option',
+      });
+    }
+
+    const isFirstSelectableElement = () => {
+      if (value) {
+        return selected;
+      }
+      const firstSelectableElement = arr.find(
+        (item) => item.props.value !== undefined && item.props.disabled !== true,
+      );
+      if (child === firstSelectableElement) {
+        return true;
+      }
+      return selected;
+    };
+
     return React.cloneElement(child, {
       'aria-selected': selected ? 'true' : 'false',
       onClick: handleItemClick(child),
@@ -405,7 +425,10 @@ const SelectInput = React.forwardRef(function SelectInput(props, ref) {
         }
       },
       role: 'option',
-      selected,
+      selected:
+        arr[0].props.value === undefined || arr[0].props.disabled === true
+          ? isFirstSelectableElement()
+          : selected,
       value: undefined, // The value is most likely not a valid HTML attribute.
       'data-value': child.props.value, // Instead, we provide it as a data attribute.
     });