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():
diff --git a/tests/slack_sdk/socket_mode/test_builtin.py b/tests/slack_sdk/socket_mode/test_builtin.py
index a1780a7e0..2d319b858 100644
--- a/tests/slack_sdk/socket_mode/test_builtin.py
+++ b/tests/slack_sdk/socket_mode/test_builtin.py
@@ -48,6 +48,24 @@ def test_init_close(self):
         finally:
             client.close()
 
+    def test_close_shuts_down_all_runners(self):
+        # Regression for #1873: close() must shut down current_session_runner
+        # along with current_app_monitor and message_processor. Previously
+        # current_session_runner was left running (100 ms loop), so each
+        # init/close cycle leaked one thread.
+        client = SocketModeClient(app_token="xapp-A111-222-xyz")
+        # The first two runners are started inside __init__.
+        self.assertTrue(client.current_session_runner.is_alive())
+        self.assertTrue(client.message_processor.is_alive())
+        client.close()
+        # IntervalRunner.shutdown() joins the thread, so by the time
+        # close() returns these are no longer alive.
+        self.assertFalse(client.current_session_runner.is_alive())
+        self.assertFalse(client.message_processor.is_alive())
+        # current_app_monitor is only started in connect(); since this test
+        # never connects, it should report not-alive both before and after.
+        self.assertFalse(client.current_app_monitor.is_alive())
+
     def test_issue_new_wss_url(self):
         client = SocketModeClient(
             app_token="xapp-A111-222-xyz",