diff --git a/starlette/middleware/gzip.py b/starlette/middleware/gzip.py
index b677063da..875198e52 100644
--- a/starlette/middleware/gzip.py
+++ b/starlette/middleware/gzip.py
@@ -81,6 +81,7 @@ async def send_with_gzip(self, message: Message) -> None:
                 del headers["Content-Length"]
 
                 self.gzip_file.write(body)
+                self.gzip_file.flush()
                 message["body"] = self.gzip_buffer.getvalue()
                 self.gzip_buffer.seek(0)
                 self.gzip_buffer.truncate()
@@ -94,7 +95,9 @@ async def send_with_gzip(self, message: Message) -> None:
             more_body = message.get("more_body", False)
 
             self.gzip_file.write(body)
-            if not more_body:
+            if more_body:
+                self.gzip_file.flush()
+            else:
                 self.gzip_file.close()
 
             message["body"] = self.gzip_buffer.getvalue()
diff --git a/tests/middleware/test_gzip.py b/tests/middleware/test_gzip.py
index b20a7cb84..6c5f60247 100644
--- a/tests/middleware/test_gzip.py
+++ b/tests/middleware/test_gzip.py
@@ -1,9 +1,12 @@
+from __future__ import annotations
+
 from starlette.applications import Starlette
 from starlette.middleware import Middleware
 from starlette.middleware.gzip import GZipMiddleware
 from starlette.requests import Request
 from starlette.responses import ContentStream, PlainTextResponse, StreamingResponse
 from starlette.routing import Route
+from starlette.types import ASGIApp, Message, Receive, Scope, Send
 from tests.types import TestClientFactory
 
 
@@ -61,6 +64,24 @@ def homepage(request: Request) -> PlainTextResponse:
 
 
 def test_gzip_streaming_response(test_client_factory: TestClientFactory) -> None:
+    class VerifyingMiddleware:
+        def __init__(self, app: ASGIApp) -> None:
+            self.app = app
+
+        async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
+            self.send = send
+            self.received_chunks: list[bytes] = []
+            await self.app(scope, receive, self.sent_from_gzip)
+            assert all(chunk != b"" for chunk in self.received_chunks)
+            assert len(self.received_chunks) == 11
+
+        async def sent_from_gzip(self, message: Message) -> None:
+            message_type = message["type"]
+            if message_type == "http.response.body":
+                body = message.get("body", b"")
+                self.received_chunks.append(body)
+            await self.send(message)
+
     def homepage(request: Request) -> StreamingResponse:
         async def generator(bytes: bytes, count: int) -> ContentStream:
             for index in range(count):
@@ -71,7 +92,10 @@ async def generator(bytes: bytes, count: int) -> ContentStream:
 
     app = Starlette(
         routes=[Route("/", endpoint=homepage)],
-        middleware=[Middleware(GZipMiddleware)],
+        middleware=[
+            Middleware(VerifyingMiddleware),
+            Middleware(GZipMiddleware),
+        ],
     )
 
     client = test_client_factory(app)