diff --git a/distributed/tests/test_worker.py b/distributed/tests/test_worker.py
index 6bea4a3fdf5..9346da09e95 100644
--- a/distributed/tests/test_worker.py
+++ b/distributed/tests/test_worker.py
@@ -3550,3 +3550,37 @@ async def test_broken_comm(c, s, a, b):
     )
     s = df.shuffle("id", shuffle="tasks")
     await c.compute(s.size)
+
+
+@gen_cluster(nthreads=[])
+async def test_do_not_block_event_loop_during_shutdown(s):
+    loop = asyncio.get_running_loop()
+    called_handler = threading.Event()
+    block_handler = threading.Event()
+
+    w = await Worker(s.address)
+    executor = w.executors["default"]
+
+    # The block wait must be smaller than the test timeout and smaller than the
+    # default value for timeout in `Worker.close``
+    async def block():
+        def fn():
+            called_handler.set()
+            assert block_handler.wait(20)
+
+        await loop.run_in_executor(executor, fn)
+
+    async def set_future():
+        while True:
+            try:
+                await loop.run_in_executor(executor, sleep, 0.1)
+            except RuntimeError:  # executor has started shutting down
+                block_handler.set()
+                return
+
+    async def close():
+        called_handler.wait()
+        # executor_wait is True by default but we want to be explicit here
+        await w.close(executor_wait=True)
+
+    await asyncio.gather(block(), close(), set_future())
diff --git a/distributed/worker.py b/distributed/worker.py
index e5563ed09d7..6a18bd1cd75 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -53,7 +53,7 @@
 from distributed.comm import connect, get_address_host
 from distributed.comm.addressing import address_from_user_args, parse_address
 from distributed.comm.utils import OFFLOAD_THRESHOLD
-from distributed.compatibility import randbytes
+from distributed.compatibility import randbytes, to_thread
 from distributed.core import (
     CommClosedError,
     ConnectionPool,
@@ -1525,11 +1525,19 @@ async def close(
         for executor in self.executors.values():
             if executor is utils._offload_executor:
                 continue  # Never shutdown the offload executor
-            if isinstance(executor, ThreadPoolExecutor):
-                executor._work_queue.queue.clear()
-                executor.shutdown(wait=executor_wait, timeout=timeout)
-            else:
-                executor.shutdown(wait=executor_wait)
+
+            def _close():
+                if isinstance(executor, ThreadPoolExecutor):
+                    executor._work_queue.queue.clear()
+                    executor.shutdown(wait=executor_wait, timeout=timeout)
+                else:
+                    executor.shutdown(wait=executor_wait)
+
+            # Waiting for the shutdown can block the event loop causing
+            # weird deadlocks particularly if the task that is executing in
+            # the thread is waiting for a server reply, e.g. when using
+            # worker clients, semaphores, etc.
+            await to_thread(_close)
 
         self.stop()
         await self.rpc.close()