diff --git a/httpx/_client.py b/httpx/_client.py
index 13cd933673..aabb03897a 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -1726,8 +1726,13 @@ async def _send_single_request(self, request: Request) -> Response:
                 "Attempted to send a sync request with an AsyncClient instance."
             )
 
-        with request_context(request=request):
-            response = await transport.handle_async_request(request)
+        try:
+            with request_context(request=request):
+                response = await transport.handle_async_request(request)
+        except BaseException:
+            if hasattr(request.stream, "aclose"):
+                await request.stream.aclose()
+            raise
 
         assert isinstance(response.stream, AsyncByteStream)
         response.request = request
diff --git a/httpx/_content.py b/httpx/_content.py
index 6f479a0885..1112870bd1 100644
--- a/httpx/_content.py
+++ b/httpx/_content.py
@@ -28,15 +28,39 @@
 __all__ = ["ByteStream"]
 
 
+class _ByteStreamIterator:
+    def __init__(self, data: bytes) -> None:
+        self._data = data
+        self._consumed = False
+
+    def __aiter__(self) -> AsyncIterator[bytes]:
+        return self
+
+    async def __anext__(self) -> bytes:
+        if self._consumed:
+            raise StopAsyncIteration
+        self._consumed = True
+        return self._data
+
+    async def aclose(self) -> None:
+        self._consumed = True
+
+
 class ByteStream(AsyncByteStream, SyncByteStream):
     def __init__(self, stream: bytes) -> None:
         self._stream = stream
+        self._iterator: _ByteStreamIterator | None = None
 
     def __iter__(self) -> Iterator[bytes]:
         yield self._stream
 
-    async def __aiter__(self) -> AsyncIterator[bytes]:
-        yield self._stream
+    def __aiter__(self) -> AsyncIterator[bytes]:
+        self._iterator = _ByteStreamIterator(self._stream)
+        return self._iterator
+
+    async def aclose(self) -> None:
+        if self._iterator is not None:
+            await self._iterator.aclose()
 
 
 class IteratorByteStream(SyncByteStream):