diff --git a/starlette/responses.py b/starlette/responses.py
index 15292f0e7..047ff9561 100644
--- a/starlette/responses.py
+++ b/starlette/responses.py
@@ -207,7 +207,7 @@ def __init__(
         self.headers["location"] = quote(str(url), safe=":/%#?=@[]!$&'()*+,;")
 
 
-Content = typing.Union[str, bytes]
+Content = typing.Union[str, bytes, memoryview]
 SyncContentStream = typing.Iterable[Content]
 AsyncContentStream = typing.AsyncIterable[Content]
 ContentStream = typing.Union[AsyncContentStream, SyncContentStream]
@@ -248,7 +248,7 @@ async def stream_response(self, send: Send) -> None:
             }
         )
         async for chunk in self.body_iterator:
-            if not isinstance(chunk, bytes):
+            if not isinstance(chunk, (bytes, memoryview)):
                 chunk = chunk.encode(self.charset)
             await send({"type": "http.response.body", "body": chunk, "more_body": True})
 
diff --git a/tests/test_responses.py b/tests/test_responses.py
index a3cdcadcf..fa3c1009f 100644
--- a/tests/test_responses.py
+++ b/tests/test_responses.py
@@ -541,6 +541,13 @@ def test_streaming_response_known_size(test_client_factory: TestClientFactory) -
     assert response.headers["content-length"] == "10"
 
 
+def test_streaming_response_memoryview(test_client_factory: TestClientFactory) -> None:
+    app = StreamingResponse(content=iter([memoryview(b"hello"), memoryview(b"world")]))
+    client: TestClient = test_client_factory(app)
+    response = client.get("/")
+    assert response.text == "helloworld"
+
+
 @pytest.mark.anyio
 async def test_streaming_response_stops_if_receiving_http_disconnect() -> None:
     streamed = 0