diff --git a/moto/rds/models.py b/moto/rds/models.py
index 1ac46d05a..1237d167e 100644
--- a/moto/rds/models.py
+++ b/moto/rds/models.py
@@ -1818,7 +1818,13 @@ class RDSBackend(BaseBackend):
         db_instance = self.describe_db_instances(
             db_instance_identifier=source_db_identifier
         )[0]
-        new_instance_props = copy.deepcopy(db_instance.__dict__)
+
+        # remove the db subnet group as it cannot be copied
+        # and is not used in the restored instance
+        source_dict = db_instance.__dict__
+        del source_dict["db_subnet_group"]
+
+        new_instance_props = copy.deepcopy(source_dict)
         if not db_instance.option_group_supplied:
             # If the option group is not supplied originally, the 'option_group_name' will receive a default value
             # Force this reconstruction, and prevent any validation on the default value