diff --git a/sentry_sdk/integrations/celery/__init__.py b/sentry_sdk/integrations/celery/__init__.py
index d9e9188090..a3b00a90c7 100644
--- a/sentry_sdk/integrations/celery/__init__.py
+++ b/sentry_sdk/integrations/celery/__init__.py
@@ -337,7 +337,8 @@ def _inner(*args, **kwargs):
                 op=OP.QUEUE_PROCESS, description=task.name
             ) as span:
                 _set_messaging_destination_name(task, span)
-                span.set_data("messaging.message.id", task.request.id)
+                with capture_internal_exceptions():
+                    span.set_data("messaging.message.id", task.request.id)
                 with capture_internal_exceptions():
                     span.set_data("messaging.message.retry.count", task.request.retries)
                 return f(*args, **kwargs)