diff --git a/aioboto3/s3/inject.py b/aioboto3/s3/inject.py
index 4f512b6..ffb7b3b 100644
--- a/aioboto3/s3/inject.py
+++ b/aioboto3/s3/inject.py
@@ -263,7 +263,7 @@ async def file_reader() -> None:
         nonlocal exception
         part = 0
         eof = False
-        while not eof:
+        while not exception and not eof:
             part += 1
             multipart_payload = bytearray()
             loop_counter = 0