diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index b749e210a..b1ab2c079 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -248,6 +248,7 @@ async def _handle_resumption_request(self, ctx: RequestContext) -> None:
                     ctx.metadata.on_resumption_token_update if ctx.metadata else None,
                 )
                 if is_complete:
+                    await event_source.response.aclose()
                     break
 
     async def _handle_post_request(self, ctx: RequestContext) -> None:
@@ -330,6 +331,7 @@ async def _handle_sse_response(
                 # If the SSE event indicates completion, like returning respose/error
                 # break the loop
                 if is_complete:
+                    await response.aclose()
                     break
         except Exception as e:
             logger.exception("Error reading SSE stream:")