diff --git a/airflow/providers/openlineage/plugins/adapter.py b/airflow/providers/openlineage/plugins/adapter.py
index 339ad55fdd2ce..348f83ee6a193 100644
--- a/airflow/providers/openlineage/plugins/adapter.py
+++ b/airflow/providers/openlineage/plugins/adapter.py
@@ -295,11 +295,17 @@ def fail_task(
         """
         error_facet = {}
         if error:
-            if isinstance(error, BaseException):
+            stack_trace = None
+            if isinstance(error, BaseException) and error.__traceback__:
                 import traceback
 
-                error = "\\n".join(traceback.format_exception(type(error), error, error.__traceback__))
-            error_facet = {"errorMessage": ErrorMessageRunFacet(message=error, programmingLanguage="python")}
+                stack_trace = "\\n".join(traceback.format_exception(type(error), error, error.__traceback__))
+
+            error_facet = {
+                "errorMessage": ErrorMessageRunFacet(
+                    message=str(error), programmingLanguage="python", stackTrace=stack_trace
+                )
+            }
 
         event = RunEvent(
             eventType=RunState.FAIL,
diff --git a/tests/providers/openlineage/plugins/test_adapter.py b/tests/providers/openlineage/plugins/test_adapter.py
index 1242bb3ef98b0..d548e03a91be9 100644
--- a/tests/providers/openlineage/plugins/test_adapter.py
+++ b/tests/providers/openlineage/plugins/test_adapter.py
@@ -457,6 +457,7 @@ def test_emit_failed_event_with_additional_information(mock_stats_incr, mock_sta
             run_facets={"externalQuery": ExternalQueryRunFacet(externalQueryId="123", source="source")},
             job_facets={"sql": SqlJobFacet(query="SELECT 1;")},
         ),
+        error=ValueError("Error message"),
     )
 
     assert (
@@ -476,6 +477,9 @@ def test_emit_failed_event_with_additional_information(mock_stats_incr, mock_sta
                             job={"namespace": namespace(), "name": "parent_job_name"},
                         ),
                         "externalQuery": ExternalQueryRunFacet(externalQueryId="123", source="source"),
+                        "errorMessage": ErrorMessageRunFacet(
+                            message="Error message", programmingLanguage="python", stackTrace=None
+                        ),
                     },
                 ),
                 job=Job(