diff --git a/slack_sdk/socket_mode/aiohttp/__init__.py b/slack_sdk/socket_mode/aiohttp/__init__.py
index a31fd2c15..da104b50e 100644
--- a/slack_sdk/socket_mode/aiohttp/__init__.py
+++ b/slack_sdk/socket_mode/aiohttp/__init__.py
@@ -349,7 +349,7 @@ async def connect(self):
         # a new monitor and a new message receiver are also created.
         # If a new session is created but we failed to create the new
         # monitor or the new message, we should try it.
-        while True:
+        while not self.closed:
             try:
                 old_session: Optional[ClientWebSocketResponse] = (
                     None if self.current_session is None else self.current_session
@@ -405,6 +405,10 @@ async def connect(self):
                     self.logger.debug(f"A new receive_messages() executor has been recreated for {session_id}")
                 break
             except Exception as e:
+                if self.closed:
+                    if self.logger.level <= logging.DEBUG:
+                        self.logger.debug(f"Stopped connecting because the client is closed (error: {e})")
+                    return
                 self.logger.exception(f"Failed to connect (error: {e}); Retrying...")
                 await asyncio.sleep(self.ping_interval)
 
diff --git a/tests/slack_sdk_async/socket_mode/test_aiohttp.py b/tests/slack_sdk_async/socket_mode/test_aiohttp.py
index eda1fecdd..4834c0c84 100644
--- a/tests/slack_sdk_async/socket_mode/test_aiohttp.py
+++ b/tests/slack_sdk_async/socket_mode/test_aiohttp.py
@@ -1,5 +1,7 @@
 import asyncio
+import logging
 import unittest
+from unittest.mock import MagicMock
 
 from slack_sdk.socket_mode.aiohttp import SocketModeClient
 from slack_sdk.web.async_client import AsyncWebClient
@@ -31,6 +33,41 @@ async def test_init_close(self):
         finally:
             await client.close()
 
+    @async_test
+    async def test_connect_returns_when_closed(self):
+        # Regression test for #1913: connect() must not loop forever once the client is closed.
+        client = SocketModeClient(
+            app_token="xapp-A111-222-xyz",
+            web_client=self.web_client,
+            auto_reconnect_enabled=False,
+            ping_interval=0.01,
+        )
+        client.wss_uri = "ws://localhost:8888/link"
+        await client.close()
+        await asyncio.wait_for(client.connect(), timeout=1.0)
+        self.assertTrue(client.closed)
+
+    @async_test
+    async def test_connect_returns_when_exception_raised_after_close(self):
+        client = SocketModeClient(
+            app_token="xapp-A111-222-xyz",
+            web_client=self.web_client,
+            auto_reconnect_enabled=False,
+            ping_interval=0.01,
+        )
+        client.logger = MagicMock()
+        client.logger.level = logging.DEBUG
+
+        async def close_then_raise(*args, **kwargs):
+            await client.close()
+            raise RuntimeError("Session is closed")
+
+        client.issue_new_wss_url = close_then_raise
+
+        await asyncio.wait_for(client.connect(), timeout=1.0)
+        self.assertTrue(client.closed)
+        client.logger.exception.assert_not_called()
+
     @async_test
     async def test_init_with_loop(self):
         client = SocketModeClient(