diff --git a/slack_sdk/socket_mode/builtin/client.py b/slack_sdk/socket_mode/builtin/client.py
index a5e902b5e..132de10db 100644
--- a/slack_sdk/socket_mode/builtin/client.py
+++ b/slack_sdk/socket_mode/builtin/client.py
@@ -221,10 +221,13 @@ def send_message(self, message: str) -> None:
                     )
                     raise e
 
-    def close(self):
+    def close(self) -> None:
         self.closed = True
         self.auto_reconnect_enabled = False
+        self.current_session_state.terminated = True
         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_interactions_builtin.py b/tests/slack_sdk/socket_mode/test_interactions_builtin.py
index 3f53e4cd1..216453afe 100644
--- a/tests/slack_sdk/socket_mode/test_interactions_builtin.py
+++ b/tests/slack_sdk/socket_mode/test_interactions_builtin.py
@@ -145,3 +145,25 @@ def test_send_message_while_disconnection(self):
             client.send_message("foo")
         finally:
             client.close()
+
+    def test_close_reaps_current_session_runner(self):
+        # Regression for #1873: close() must reap current_session_runner without hanging.
+        client = SocketModeClient(
+            app_token="xapp-A111-222-xyz",
+            web_client=self.web_client,
+            auto_reconnect_enabled=False,
+            trace_enabled=True,
+        )
+        try:
+            client.wss_uri = "ws://0.0.0.0:3011/link"
+            client.connect()
+            self.assertTrue(client.is_connected())
+            time.sleep(1)
+
+            client.close()
+
+            self.assertFalse(client.current_session_runner.is_alive())
+            self.assertFalse(client.current_app_monitor.is_alive())
+            self.assertFalse(client.message_processor.is_alive())
+        finally:
+            client.close()