diff --git a/airflow/models/taskinstance.py b/airflow/models/taskinstance.py
index 1b76145a469e2..e39f54a8bb0f3 100644
--- a/airflow/models/taskinstance.py
+++ b/airflow/models/taskinstance.py
@@ -1360,18 +1360,27 @@ def _run_finished_callback(self, error: Optional[Union[str, Exception]] = None)
             if task.on_failure_callback is not None:
                 context = self.get_template_context()
                 context["exception"] = error
-                task.on_failure_callback(context)
+                try:
+                    task.on_failure_callback(context)
+                except Exception:
+                    self.log.exception("Error when executing on_failure_callback")
         elif self.state == State.SUCCESS:
             task = self.task
             if task.on_success_callback is not None:
                 context = self.get_template_context()
-                task.on_success_callback(context)
+                try:
+                    task.on_success_callback(context)
+                except Exception:
+                    self.log.exception("Error when executing on_success_callback")
         elif self.state == State.UP_FOR_RETRY:
             task = self.task
             if task.on_retry_callback is not None:
                 context = self.get_template_context()
                 context["exception"] = error
-                task.on_retry_callback(context)
+                try:
+                    task.on_retry_callback(context)
+                except Exception:
+                    self.log.exception("Error when executing on_retry_callback")
 
     @provide_session
     def run(
diff --git a/tests/models/test_taskinstance.py b/tests/models/test_taskinstance.py
index 7d64c76c5a92f..2e5eb8a88d43c 100644
--- a/tests/models/test_taskinstance.py
+++ b/tests/models/test_taskinstance.py
@@ -1743,6 +1743,45 @@ def on_execute_callable(context):
         ti.refresh_from_db()
         assert ti.state == State.SUCCESS
 
+    @parameterized.expand(
+        [
+            (State.SUCCESS, "Error when executing on_success_callback"),
+            (State.UP_FOR_RETRY, "Error when executing on_retry_callback"),
+            (State.FAILED, "Error when executing on_failure_callback"),
+        ]
+    )
+    def test_finished_callbacks_handle_and_log_exception(self, finished_state, expected_message):
+        called = completed = False
+
+        def on_finish_callable(context):
+            nonlocal called, completed
+            called = True
+            raise KeyError
+            completed = True
+
+        dag = DAG(
+            'test_success_callback_handles_exception',
+            start_date=DEFAULT_DATE,
+            end_date=DEFAULT_DATE + datetime.timedelta(days=10),
+        )
+        task = DummyOperator(
+            task_id='op',
+            email='test@test.test',
+            on_success_callback=on_finish_callable,
+            on_retry_callback=on_finish_callable,
+            on_failure_callback=on_finish_callable,
+            dag=dag,
+        )
+
+        ti = TI(task=task, execution_date=datetime.datetime.now())
+        ti._log = mock.Mock()
+        ti.state = finished_state
+        ti._run_finished_callback()
+
+        assert called
+        assert not completed
+        ti.log.exception.assert_called_once_with(expected_message)
+
     def test_handle_failure(self):
         start_date = timezone.datetime(2016, 6, 1)
         dag = models.DAG(dag_id="test_handle_failure", schedule_interval=None, start_date=start_date)