diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index cb5318a8231..5e7f4385aa1 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -3368,7 +3368,10 @@ async def close(self):
         setproctitle("dask-scheduler [closing]")
 
         for preload in self.preloads:
-            await preload.teardown()
+            try:
+                await preload.teardown()
+            except Exception as e:
+                logger.exception(e)
 
         await asyncio.gather(
             *[plugin.close() for plugin in list(self.plugins.values())]
diff --git a/distributed/tests/test_preload.py b/distributed/tests/test_preload.py
index 0bb73dd0d15..7a4185f7621 100644
--- a/distributed/tests/test_preload.py
+++ b/distributed/tests/test_preload.py
@@ -302,3 +302,14 @@ def dask_setup(client, value):
     ):
         async with Client(address=s.address, asynchronous=True) as c:
             assert c.foo == value
+
+
+@gen_test()
+async def test_teardown_failure_doesnt_crash_scheduler():
+    text = """
+def dask_teardown(worker):
+    raise Exception(123)
+"""
+    async with Scheduler(dashboard_address=":0", preload=text) as s:
+        async with Worker(s.address, preload=[text]) as w:
+            pass
diff --git a/distributed/worker.py b/distributed/worker.py
index 1795bb80c59..c146cb56fff 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -1489,7 +1489,10 @@ async def close(
                 )
 
         for preload in self.preloads:
-            await preload.teardown()
+            try:
+                await preload.teardown()
+            except Exception as e:
+                logger.exception(e)
 
         for extension in self.extensions.values():
             if hasattr(extension, "close"):