diff --git a/CHANGES b/CHANGES
index 09babb706f..e83660d6ac 100644
--- a/CHANGES
+++ b/CHANGES
@@ -1,3 +1,4 @@
+    * Add test and fix async HiredisParser when reading during a disconnect() (#2349)
     * Use hiredis-py pack_command if available.
     * Support `.unlink()` in ClusterPipeline
     * Simplify synchronous SocketBuffer state management
diff --git a/redis/asyncio/connection.py b/redis/asyncio/connection.py
index 2c75d4fcf1..862f6f096b 100644
--- a/redis/asyncio/connection.py
+++ b/redis/asyncio/connection.py
@@ -350,13 +350,14 @@ async def _readline(self) -> bytes:
 class HiredisParser(BaseParser):
     """Parser class for connections using Hiredis"""
 
-    __slots__ = BaseParser.__slots__ + ("_reader",)
+    __slots__ = BaseParser.__slots__ + ("_reader", "_connected")
 
     def __init__(self, socket_read_size: int):
         if not HIREDIS_AVAILABLE:
             raise RedisError("Hiredis is not available.")
         super().__init__(socket_read_size=socket_read_size)
         self._reader: Optional[hiredis.Reader] = None
+        self._connected: bool = False
 
     def on_connect(self, connection: "Connection"):
         self._stream = connection._reader
@@ -369,13 +370,13 @@ def on_connect(self, connection: "Connection"):
             kwargs["errors"] = connection.encoder.encoding_errors
 
         self._reader = hiredis.Reader(**kwargs)
+        self._connected = True
 
     def on_disconnect(self):
-        self._stream = None
-        self._reader = None
+        self._connected = False
 
     async def can_read_destructive(self):
-        if not self._stream or not self._reader:
+        if not self._connected:
             raise ConnectionError(SERVER_CLOSED_CONNECTION_ERROR)
         if self._reader.gets():
             return True
@@ -397,8 +398,10 @@ async def read_from_socket(self):
     async def read_response(
         self, disable_decoding: bool = False
     ) -> Union[EncodableT, List[EncodableT]]:
-        if not self._stream or not self._reader:
-            self.on_disconnect()
+        # If `on_disconnect()` has been called, prohibit any more reads
+        # even if they could happen because data might be present.
+        # We still allow reads in progress to finish
+        if not self._connected:
             raise ConnectionError(SERVER_CLOSED_CONNECTION_ERROR) from None
 
         response = self._reader.gets()
diff --git a/tests/test_asyncio/test_connection.py b/tests/test_asyncio/test_connection.py
index 8e4fdac309..1851ca9a76 100644
--- a/tests/test_asyncio/test_connection.py
+++ b/tests/test_asyncio/test_connection.py
@@ -10,12 +10,14 @@
 from redis.asyncio.connection import (
     BaseParser,
     Connection,
+    HiredisParser,
     PythonParser,
     UnixDomainSocketConnection,
 )
 from redis.asyncio.retry import Retry
 from redis.backoff import NoBackoff
 from redis.exceptions import ConnectionError, InvalidResponse, TimeoutError
+from redis.utils import HIREDIS_AVAILABLE
 from tests.conftest import skip_if_server_version_lt
 
 from .compat import mock
@@ -191,3 +193,83 @@ async def test_connection_parse_response_resume(r: redis.Redis):
         pytest.fail("didn't receive a response")
     assert response
     assert i > 0
+
+
+@pytest.mark.onlynoncluster
+@pytest.mark.parametrize(
+    "parser_class", [PythonParser, HiredisParser], ids=["PythonParser", "HiredisParser"]
+)
+async def test_connection_disconect_race(parser_class):
+    """
+    This test reproduces the case in issue #2349
+    where a connection is closed while the parser is reading to feed the
+    internal buffer.The stream `read()` will succeed, but when it returns,
+    another task has already called `disconnect()` and is waiting for
+    close to finish.  When we attempts to feed the buffer, we will fail
+    since the buffer is no longer there.
+
+    This test verifies that a read in progress can finish even
+    if the `disconnect()` method is called.
+    """
+    if parser_class == PythonParser:
+        pytest.xfail("doesn't work yet with PythonParser")
+    if parser_class == HiredisParser and not HIREDIS_AVAILABLE:
+        pytest.skip("Hiredis not available")
+
+    args = {}
+    args["parser_class"] = parser_class
+
+    conn = Connection(**args)
+
+    cond = asyncio.Condition()
+    # 0 == initial
+    # 1 == reader is reading
+    # 2 == closer has closed and is waiting for close to finish
+    state = 0
+
+    # Mock read function, which wait for a close to happen before returning
+    # Can either be invoked as two `read()` calls (HiredisParser)
+    # or as a `readline()` followed by `readexact()` (PythonParser)
+    chunks = [b"$13\r\n", b"Hello, World!\r\n"]
+
+    async def read(_=None):
+        nonlocal state
+        async with cond:
+            if state == 0:
+                state = 1  # we are reading
+                cond.notify()
+                # wait until the closing task has done
+                await cond.wait_for(lambda: state == 2)
+        return chunks.pop(0)
+
+    # function closes the connection while reader is still blocked reading
+    async def do_close():
+        nonlocal state
+        async with cond:
+            await cond.wait_for(lambda: state == 1)
+            state = 2
+            cond.notify()
+        await conn.disconnect()
+
+    async def do_read():
+        return await conn.read_response()
+
+    reader = mock.AsyncMock()
+    writer = mock.AsyncMock()
+    writer.transport = mock.Mock()
+    writer.transport.get_extra_info.side_effect = None
+
+    # for HiredisParser
+    reader.read.side_effect = read
+    # for PythonParser
+    reader.readline.side_effect = read
+    reader.readexactly.side_effect = read
+
+    async def open_connection(*args, **kwargs):
+        return reader, writer
+
+    with patch.object(asyncio, "open_connection", open_connection):
+        await conn.connect()
+
+    vals = await asyncio.gather(do_read(), do_close())
+    assert vals == [b"Hello, World!", None]