diff --git a/httpx/_content.py b/httpx/_content.py
index d7e8aa0974..9032c1c056 100644
--- a/httpx/_content.py
+++ b/httpx/_content.py
@@ -38,6 +38,8 @@ async def __aiter__(self) -> AsyncIterator[bytes]:
 
 
 class IteratorByteStream(SyncByteStream):
+    CHUNK_SIZE = 65_536
+
     def __init__(self, stream: Iterable[bytes]):
         self._stream = stream
         self._is_stream_consumed = False
@@ -48,11 +50,21 @@ def __iter__(self) -> Iterator[bytes]:
             raise StreamConsumed()
 
         self._is_stream_consumed = True
-        for part in self._stream:
-            yield part
+        if hasattr(self._stream, "read"):
+            # File-like interfaces should use 'read' directly.
+            chunk = self._stream.read(self.CHUNK_SIZE)  # type: ignore
+            while chunk:
+                yield chunk
+                chunk = self._stream.read(self.CHUNK_SIZE)  # type: ignore
+        else:
+            # Otherwise iterate.
+            for part in self._stream:
+                yield part
 
 
 class AsyncIteratorByteStream(AsyncByteStream):
+    CHUNK_SIZE = 65_536
+
     def __init__(self, stream: AsyncIterable[bytes]):
         self._stream = stream
         self._is_stream_consumed = False
@@ -63,8 +75,16 @@ async def __aiter__(self) -> AsyncIterator[bytes]:
             raise StreamConsumed()
 
         self._is_stream_consumed = True
-        async for part in self._stream:
-            yield part
+        if hasattr(self._stream, "aread"):
+            # File-like interfaces should use 'aread' directly.
+            chunk = await self._stream.aread(self.CHUNK_SIZE)  # type: ignore
+            while chunk:
+                yield chunk
+                chunk = await self._stream.aread(self.CHUNK_SIZE)  # type: ignore
+        else:
+            # Otherwise iterate.
+            async for part in self._stream:
+                yield part
 
 
 class UnattachedStream(AsyncByteStream, SyncByteStream):
diff --git a/httpx/_multipart.py b/httpx/_multipart.py
index 4dfb838a68..f05f02b4c5 100644
--- a/httpx/_multipart.py
+++ b/httpx/_multipart.py
@@ -71,6 +71,8 @@ class FileField:
     A single file field item, within a multipart form field.
     """
 
+    CHUNK_SIZE = 64 * 1024
+
     def __init__(self, name: str, value: FileTypes) -> None:
         self.name = name
 
@@ -142,8 +144,10 @@ def render_data(self) -> typing.Iterator[bytes]:
             self.file.seek(0)
         self._consumed = True
 
-        for chunk in self.file:
+        chunk = self.file.read(self.CHUNK_SIZE)
+        while chunk:
             yield to_bytes(chunk)
+            chunk = self.file.read(self.CHUNK_SIZE)
 
     def render(self) -> typing.Iterator[bytes]:
         yield self.render_headers()
diff --git a/tests/test_content.py b/tests/test_content.py
index 2a273a133f..afd910399e 100644
--- a/tests/test_content.py
+++ b/tests/test_content.py
@@ -60,6 +60,31 @@ async def test_bytesio_content():
     assert content == b"Hello, world!"
 
 
+@pytest.mark.asyncio
+async def test_async_bytesio_content():
+    class AsyncBytesIO:
+        def __init__(self, content):
+            self._idx = 0
+            self._content = content
+
+        async def aread(self, chunk_size: int):
+            chunk = self._content[self._idx : self._idx + chunk_size]
+            self._idx = self._idx + chunk_size
+            return chunk
+
+        async def __aiter__(self):
+            yield self._content  # pragma: nocover
+
+    headers, stream = encode_request(content=AsyncBytesIO(b"Hello, world!"))
+    assert not isinstance(stream, typing.Iterable)
+    assert isinstance(stream, typing.AsyncIterable)
+
+    content = b"".join([part async for part in stream])
+
+    assert headers == {"Transfer-Encoding": "chunked"}
+    assert content == b"Hello, world!"
+
+
 @pytest.mark.asyncio
 async def test_iterator_content():
     def hello_world():