diff --git a/telegram/ext/_updater.py b/telegram/ext/_updater.py
index 95133d075..536b4f443 100644
--- a/telegram/ext/_updater.py
+++ b/telegram/ext/_updater.py
@@ -309,6 +309,10 @@ class Updater(AbstractAsyncContextManager):
                     pool_timeout=pool_timeout,
                     allowed_updates=allowed_updates,
                 )
+            except asyncio.CancelledError as exc:
+                # TODO: in py3.8+, CancelledError is a subclass of BaseException, so we can drop
+                #  this clause when we drop py3.7
+                raise exc
             except TelegramError as exc:
                 # TelegramErrors should be processed by the network retry loop
                 raise exc
diff --git a/telegram/request/_baserequest.py b/telegram/request/_baserequest.py
index 4f83dc5ff..72f71580a 100644
--- a/telegram/request/_baserequest.py
+++ b/telegram/request/_baserequest.py
@@ -18,6 +18,7 @@
 # along with this program.  If not, see [http://www.gnu.org/licenses/].
 """This module contains an abstract class to make POST and GET requests."""
 import abc
+import asyncio
 from contextlib import AbstractAsyncContextManager
 from http import HTTPStatus
 from types import TracebackType
@@ -275,6 +276,10 @@ class BaseRequest(
                 connect_timeout=connect_timeout,
                 pool_timeout=pool_timeout,
             )
+        except asyncio.CancelledError as exc:
+            # TODO: in py3.8+, CancelledError is a subclass of BaseException, so we can drop this
+            #  clause when we drop py3.7
+            raise exc
         except TelegramError as exc:
             raise exc
         except Exception as exc: