diff --git a/airflow-core/src/airflow/dag_processing/manager.py b/airflow-core/src/airflow/dag_processing/manager.py
index a4d4917958c11..e8a8a2c50366e 100644
--- a/airflow-core/src/airflow/dag_processing/manager.py
+++ b/airflow-core/src/airflow/dag_processing/manager.py
@@ -56,7 +56,6 @@
 from airflow.dag_processing.bundles.manager import DagBundlesManager
 from airflow.dag_processing.collection import update_dag_parsing_results_in_db
 from airflow.dag_processing.processor import DagFileParsingResult, DagFileProcessorProcess
-from airflow.exceptions import AirflowException
 from airflow.models.asset import remove_references_to_deleted_dags
 from airflow.models.dag import DagModel
 from airflow.models.dagbag import DagPriorityParsingRequest
@@ -853,7 +852,7 @@ def _refresh_dag_bundles(self, known_files: dict[str, set[DagFileInfo]]):
                 try:
                     bundle.initialize()
                     any_refreshed = True
-                except AirflowException as e:
+                except Exception as e:
                     self.log.exception("Error initializing bundle %s: %s", bundle.name, e)
                     continue
             try:
diff --git a/airflow-core/tests/unit/dag_processing/test_manager.py b/airflow-core/tests/unit/dag_processing/test_manager.py
index b136a4d9e8fe3..4599c8ea58342 100644
--- a/airflow-core/tests/unit/dag_processing/test_manager.py
+++ b/airflow-core/tests/unit/dag_processing/test_manager.py
@@ -3251,6 +3251,39 @@ def test_refresh_dag_bundles_get_bundle_state_failure_skips_bundle(self):
 
         bundle.refresh.assert_not_called()
 
+    def test_refresh_dag_bundles_initialize_non_airflow_exception_skips_bundle(self):
+        """
+        A bundle whose initialize() raises a non AirflowException must be skipped, not
+        left to propagate and abort refresh for every other bundle.
+        """
+        manager = DagFileProcessorManager(max_runs=1)
+        failing_bundle = self._make_refresh_bundle()
+        failing_bundle.name = "failing_bundle"
+        failing_bundle.is_initialized = False
+        failing_bundle.initialize.side_effect = FileNotFoundError("Repository path not found")
+
+        healthy_bundle = self._make_refresh_bundle()
+        healthy_bundle.name = "healthy_bundle"
+
+        manager._dag_bundles = [failing_bundle, healthy_bundle]
+        manager._force_refresh_bundles = set()
+
+        with (
+            mock.patch.object(
+                manager, "get_bundle_state", return_value=BundleState(last_refreshed=None, version=None)
+            ),
+            mock.patch.object(manager, "update_bundle_state"),
+            mock.patch.object(manager, "_find_files_in_bundle", return_value=[]),
+            mock.patch.object(manager, "deactivate_deleted_dags"),
+            mock.patch.object(manager, "clear_orphaned_import_errors"),
+            mock.patch.object(manager, "handle_removed_files"),
+            mock.patch.object(manager, "_resort_file_queue"),
+            mock.patch.object(manager, "_add_new_files_to_queue"),
+        ):
+            manager._refresh_dag_bundles({})
+
+        healthy_bundle.refresh.assert_called_once()
+
     def test_refresh_dag_bundles_update_bundle_state_failure_still_scans_files(self):
         """A failure in update_bundle_state() logs but does not skip file scanning.