diff --git a/src/proto/h1/conn.rs b/src/proto/h1/conn.rs
index b7c619683c..3e753c6f6a 100644
--- a/src/proto/h1/conn.rs
+++ b/src/proto/h1/conn.rs
@@ -175,6 +175,11 @@ where
         }
     }
 
+    #[cfg(feature = "server")]
+    pub(crate) fn has_initial_read_write_state(&self) -> bool {
+        matches!(self.state.reading, Reading::Init) && matches!(self.state.writing, Writing::Init)
+    }
+
     fn should_error_on_eof(&self) -> bool {
         // If we're idle, it's probably just the connection closing gracefully.
         T::should_error_on_parse_eof() && !self.state.is_idle()
diff --git a/src/proto/h1/dispatch.rs b/src/proto/h1/dispatch.rs
index cd494581b9..beb8d0a914 100644
--- a/src/proto/h1/dispatch.rs
+++ b/src/proto/h1/dispatch.rs
@@ -28,7 +28,8 @@ pub(crate) trait Dispatch {
         self: Pin<&mut Self>,
         cx: &mut task::Context<'_>,
     ) -> Poll<Option<Result<(Self::PollItem, Self::PollBody), Self::PollError>>>;
-    fn recv_msg(&mut self, msg: crate::Result<(Self::RecvItem, IncomingBody)>) -> crate::Result<()>;
+    fn recv_msg(&mut self, msg: crate::Result<(Self::RecvItem, IncomingBody)>)
+        -> crate::Result<()>;
     fn poll_ready(&mut self, cx: &mut task::Context<'_>) -> Poll<Result<(), ()>>;
     fn should_poll(&self) -> bool;
 }
@@ -81,7 +82,11 @@ where
     #[cfg(feature = "server")]
     pub(crate) fn disable_keep_alive(&mut self) {
         self.conn.disable_keep_alive();
-        if self.conn.is_write_closed() {
+
+        // If keep alive has been disabled and no read or write has been seen on
+        // the connection yet, we must be in a state where the server is being asked to
+        // shut down before any data has been seen on the connection
+        if self.conn.is_write_closed() || self.conn.has_initial_read_write_state() {
             self.close();
         }
     }
@@ -249,7 +254,8 @@ where
                 let body = match body_len {
                     DecodedLength::ZERO => IncomingBody::empty(),
                     other => {
-                        let (tx, rx) = IncomingBody::new_channel(other, wants.contains(Wants::EXPECT));
+                        let (tx, rx) =
+                            IncomingBody::new_channel(other, wants.contains(Wants::EXPECT));
                         self.body_tx = Some(tx);
                         rx
                     }
diff --git a/tests/server.rs b/tests/server.rs
index 632ce4839a..759843e291 100644
--- a/tests/server.rs
+++ b/tests/server.rs
@@ -31,6 +31,7 @@ use hyper::body::{Body, Incoming as IncomingBody};
 use hyper::server::conn::{http1, http2};
 use hyper::service::{service_fn, Service};
 use hyper::{Method, Request, Response, StatusCode, Uri, Version};
+use tokio::pin;
 
 mod support;
 
@@ -2136,6 +2137,31 @@ async fn max_buf_size() {
         .expect_err("should TooLarge error");
 }
 
+#[cfg(feature = "http1")]
+#[tokio::test]
+async fn graceful_shutdown_before_first_request_no_block() {
+    let (listener, addr) = setup_tcp_listener();
+
+    tokio::spawn(async move {
+        let socket = listener.accept().await.unwrap().0;
+
+        let future = http1::Builder::new().serve_connection(socket, HelloWorld);
+        pin!(future);
+        future.as_mut().graceful_shutdown();
+
+        future.await.unwrap();
+    });
+
+    let mut stream = TkTcpStream::connect(addr).await.unwrap();
+
+    let mut buf = vec![];
+
+    tokio::time::timeout(Duration::from_secs(5), stream.read_to_end(&mut buf))
+        .await
+        .expect("timed out waiting for graceful shutdown")
+        .expect("error receiving response");
+}
+
 #[test]
 fn streaming_body() {
     use futures_util::StreamExt;