diff --git a/tests/test_fetcher_ng.py b/tests/test_fetcher_ng.py
index 5c6de0f83e..434c62a233 100644
--- a/tests/test_fetcher_ng.py
+++ b/tests/test_fetcher_ng.py
@@ -109,11 +109,7 @@ def test_http_error(self) -> None:
     def test_response_read_timeout(self, mock_session_get: Mock) -> None:
         mock_response = Mock()
         mock_response.status = 200
-        attr = {
-            "stream.side_effect": urllib3.exceptions.ConnectionError(
-                "Simulated timeout"
-            )
-        }
+        attr = {"stream.side_effect": urllib3.exceptions.TimeoutError}
         mock_response.configure_mock(**attr)
         mock_session_get.return_value = mock_response
 
@@ -125,7 +121,11 @@ def test_response_read_timeout(self, mock_session_get: Mock) -> None:
     @patch.object(
         urllib3.PoolManager,
         "request",
-        side_effect=urllib3.exceptions.TimeoutError,
+        side_effect=urllib3.exceptions.MaxRetryError(
+            urllib3.connectionpool.ConnectionPool("localhost"),
+            "",
+            urllib3.exceptions.TimeoutError(),
+        ),
     )
     def test_session_get_timeout(self, mock_session_get: Mock) -> None:
         with self.assertRaises(exceptions.SlowRetrievalError):
diff --git a/tuf/ngclient/_internal/urllib3_fetcher.py b/tuf/ngclient/_internal/urllib3_fetcher.py
index f2c9b4f176..85cc80d5fb 100644
--- a/tuf/ngclient/_internal/urllib3_fetcher.py
+++ b/tuf/ngclient/_internal/urllib3_fetcher.py
@@ -79,8 +79,9 @@ def _fetch(self, url: str) -> Iterator[bytes]:
                 preload_content=False,
                 timeout=urllib3.Timeout(self.socket_timeout),
             )
-        except urllib3.exceptions.TimeoutError as e:
-            raise exceptions.SlowRetrievalError from e
+        except urllib3.exceptions.MaxRetryError as e:
+            if isinstance(e.reason, urllib3.exceptions.TimeoutError):
+                raise exceptions.SlowRetrievalError from e
 
         if response.status >= 400:
             response.close()
@@ -102,10 +103,7 @@ def _chunks(
 
         try:
             yield from response.stream(self.chunk_size)
-        except (
-            urllib3.exceptions.ConnectionError,
-            urllib3.exceptions.TimeoutError,
-        ) as e:
+        except urllib3.exceptions.TimeoutError as e:
             raise exceptions.SlowRetrievalError from e
 
         finally: