diff --git a/tokio/src/runtime/handle.rs b/tokio/src/runtime/handle.rs
index 7dff91448f1..4d365281129 100644
--- a/tokio/src/runtime/handle.rs
+++ b/tokio/src/runtime/handle.rs
@@ -301,7 +301,7 @@ impl Handle {
             .expect("failed to park thread")
     }
 
-    pub(crate) fn shutdown(mut self) {
+    pub(crate) fn shutdown(&mut self) {
         self.spawner.shutdown();
     }
 }
diff --git a/tokio/src/runtime/mod.rs b/tokio/src/runtime/mod.rs
index 52532ec6f12..48b1d0e7e6d 100644
--- a/tokio/src/runtime/mod.rs
+++ b/tokio/src/runtime/mod.rs
@@ -275,6 +275,9 @@ cfg_rt! {
     /// The runtime executor is either a thread-pool or a current-thread executor.
     #[derive(Debug)]
     enum Kind {
+        /// Runtime is shutting down
+        Gone,
+
         /// Execute all tasks on the current-thread.
         CurrentThread(BasicScheduler<driver::Driver>),
 
@@ -447,6 +450,7 @@ cfg_rt! {
             let _enter = self.enter();
 
             match &self.kind {
+                Kind::Gone => panic!("Runtime is shutting down"),
                 Kind::CurrentThread(exec) => exec.block_on(future),
                 #[cfg(feature = "rt-multi-thread")]
                 Kind::ThreadPool(exec) => exec.block_on(future),
@@ -560,4 +564,12 @@ cfg_rt! {
             self.shutdown_timeout(Duration::from_nanos(0))
         }
     }
+
+    impl Drop for Runtime {
+        fn drop(&mut self) {
+            let _guard = self.enter();
+            // Shutdown the runtime whilst it is still active
+            self.kind = Kind::Gone;
+        }
+    }
 }
diff --git a/tokio/tests/task_abort.rs b/tokio/tests/task_abort.rs
index 8f621683faa..f9e6651fa2e 100644
--- a/tokio/tests/task_abort.rs
+++ b/tokio/tests/task_abort.rs
@@ -1,7 +1,7 @@
 #![warn(rust_2018_idioms)]
 #![cfg(feature = "full")]
 
-use std::sync::Arc;
+use std::sync::{mpsc, Arc};
 use std::thread::sleep;
 use std::time::Duration;
 
@@ -233,3 +233,44 @@ fn test_abort_task_that_panics_on_drop_returned() {
         assert!(handle.await.unwrap_err().is_panic());
     });
 }
+
+struct SpawnOnDrop(mpsc::Sender<bool>);
+
+impl Drop for SpawnOnDrop {
+    fn drop(&mut self) {
+        let res = std::panic::catch_unwind(|| {
+            tokio::spawn(async move {
+                println!("did something");
+            });
+        });
+        self.0.send(res.is_ok()).unwrap();
+    }
+}
+
+/// Checks that aborting a task whose destructor panics has the expected result.
+#[test]
+fn test_task_that_spawns_task_on_drop() {
+    let (tx, rx) = mpsc::channel();
+
+    {
+        let rt = tokio::runtime::Builder::new_current_thread()
+            .enable_time()
+            .build()
+            .unwrap();
+
+        rt.block_on(async move {
+            let _handle = tokio::spawn(async move {
+                // Make sure the Arc is moved into the task
+                let _spawn_dropped = SpawnOnDrop(tx);
+                println!("task started");
+                tokio::time::sleep(std::time::Duration::new(1, 0)).await
+            });
+
+            // wait for task to sleep.
+            tokio::time::sleep(std::time::Duration::from_millis(10)).await;
+        });
+    }
+
+    // Check that spawning the task did not panic
+    assert!(rx.recv().unwrap());
+}