diff --git a/starlette/middleware/base.py b/starlette/middleware/base.py
index ca9deb7de..49a5e3e2d 100644
--- a/starlette/middleware/base.py
+++ b/starlette/middleware/base.py
@@ -52,7 +52,11 @@ async def body_stream() -> typing.AsyncGenerator[bytes, None]:
                 async with recv_stream:
                     async for message in recv_stream:
                         assert message["type"] == "http.response.body"
-                        yield message.get("body", b"")
+                        body = message.get("body", b"")
+                        if body:
+                            yield body
+                        if not message.get("more_body", False):
+                            break
 
                 if app_exc is not None:
                     raise app_exc