diff --git a/slack_sdk/socket_mode/builtin/client.py b/slack_sdk/socket_mode/builtin/client.py
index be80e0526..a7f21f977 100644
--- a/slack_sdk/socket_mode/builtin/client.py
+++ b/slack_sdk/socket_mode/builtin/client.py
@@ -225,6 +225,8 @@ def close(self):
         self.closed = True
         self.auto_reconnect_enabled = False
         self.disconnect()
+        if self.current_session_runner.is_alive():
+            self.current_session_runner.shutdown()
         if self.current_app_monitor.is_alive():
             self.current_app_monitor.shutdown()
         if self.message_processor.is_alive():