diff --git a/src/snowflake/connector/connection.py b/src/snowflake/connector/connection.py
index 8d6cb05a72..c6e02e154b 100644
--- a/src/snowflake/connector/connection.py
+++ b/src/snowflake/connector/connection.py
@@ -1238,7 +1238,7 @@ def __config(self, **kwargs):
                 self._token = f.read()
 
         if not (self._master_token and self._session_token):
-            if not self.user and self._authenticator != OAUTH_AUTHENTICATOR:
+            if not self.user and self._authenticator != OAUTH_AUTHENTICATOR and self._authenticator != EXTERNAL_BROWSER_AUTHENTICATOR:
                 # OAuth Authentication does not require a username
                 Error.errorhandler_wrapper(
                     self,