diff --git a/msgpack/fallback.py b/msgpack/fallback.py
index 1e0bbe91..9739d53b 100644
--- a/msgpack/fallback.py
+++ b/msgpack/fallback.py
@@ -921,7 +921,7 @@ def _pack(
                     len(obj), dict_iteritems(obj), nest_limit - 1
                 )
 
-            if self._datetime and check(obj, _DateTime):
+            if self._datetime and check(obj, _DateTime) and obj.tzinfo is not None:
                 obj = Timestamp.from_datetime(obj)
                 default_used = 1
                 continue