diff --git a/distributed/shuffle/_worker_plugin.py b/distributed/shuffle/_worker_plugin.py
index f41c9b5dfd..953042fc81 100644
--- a/distributed/shuffle/_worker_plugin.py
+++ b/distributed/shuffle/_worker_plugin.py
@@ -104,10 +104,13 @@ async def shuffle_inputs_done(self, shuffle_id: ShuffleId, run_id: int) -> None:
             await shuffle.inputs_done()
 
     async def _close_shuffle_run(self, shuffle: ShuffleRun) -> None:
-        await shuffle.close()
-        async with self._runs_cleanup_condition:
-            self._runs.remove(shuffle)
-            self._runs_cleanup_condition.notify_all()
+        with log_errors():
+            try:
+                await shuffle.close()
+            finally:
+                async with self._runs_cleanup_condition:
+                    self._runs.remove(shuffle)
+                    self._runs_cleanup_condition.notify_all()
 
     def shuffle_fail(self, shuffle_id: ShuffleId, run_id: int, message: str) -> None:
         """Fails the shuffle run with the message as exception and triggers cleanup.
@@ -277,15 +280,9 @@ async def _refresh_shuffle(
                     RuntimeError("{existing!r} stale, expected run_id=={run_id}")
                 )
 
-                async def _(
-                    extension: ShuffleWorkerPlugin, shuffle: ShuffleRun
-                ) -> None:
-                    await shuffle.close()
-                    async with extension._runs_cleanup_condition:
-                        extension._runs.remove(shuffle)
-                        extension._runs_cleanup_condition.notify_all()
-
-                self.worker._ongoing_background_tasks.call_soon(_, self, existing)
+                self.worker._ongoing_background_tasks.call_soon(
+                    ShuffleWorkerPlugin._close_shuffle_run, self, existing
+                )
         shuffle: ShuffleRun = result.spec.create_run_on_worker(
             result.run_id, result.worker_for, self
         )
diff --git a/distributed/shuffle/tests/test_shuffle.py b/distributed/shuffle/tests/test_shuffle.py
index 68f97a2558..90a5e5def6 100644
--- a/distributed/shuffle/tests/test_shuffle.py
+++ b/distributed/shuffle/tests/test_shuffle.py
@@ -3,6 +3,7 @@
 import asyncio
 import io
 import itertools
+import logging
 import os
 import random
 import shutil
@@ -610,6 +611,34 @@ async def test_closed_bystanding_worker_during_shuffle(c, s, w1, w2, w3):
     await check_scheduler_cleanup(s)
 
 
+class RaiseOnCloseShuffleRun(DataFrameShuffleRun):
+    async def close(self, *args, **kwargs):
+        raise RuntimeError("test-exception-on-close")
+
+
+@mock.patch(
+    "distributed.shuffle._shuffle.DataFrameShuffleRun",
+    RaiseOnCloseShuffleRun,
+)
+@gen_cluster(client=True, nthreads=[])
+async def test_exception_on_close_cleans_up(c, s, caplog):
+    # Ensure that everything is cleaned up and does not lock up if an exception
+    # is raised during shuffle close.
+    with caplog.at_level(logging.ERROR):
+        async with Worker(s.address) as w:
+            df = dask.datasets.timeseries(
+                start="2000-01-01",
+                end="2000-01-10",
+                dtypes={"x": float, "y": float},
+                freq="10 s",
+            )
+            shuffled = dd.shuffle.shuffle(df, "x", shuffle="p2p")
+            await c.compute([shuffled, df], sync=True)
+
+    assert any("test-exception-on-close" in record.message for record in caplog.records)
+    await check_worker_cleanup(w, closed=True)
+
+
 class BlockedInputsDoneShuffle(DataFrameShuffleRun):
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)