diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index 1d541a8e46f..80fcc8c4071 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -5232,7 +5232,8 @@ func testServerShutdown(t *testing.T, h2 bool) {
 	defer afterTest(t)
 	var doShutdown func() // set later
 	var shutdownRes = make(chan error, 1)
-	cst := newClientServerTest(t, h2, HandlerFunc(func(w ResponseWriter, r *Request) {
+	var gotOnShutdown = make(chan struct{}, 1)
+	handler := HandlerFunc(func(w ResponseWriter, r *Request) {
 		go doShutdown()
 		// Shutdown is graceful, so it should not interrupt
 		// this in-flight response. Add a tiny sleep here to
@@ -5240,7 +5241,10 @@ func testServerShutdown(t *testing.T, h2 bool) {
 		// bugs.
 		time.Sleep(20 * time.Millisecond)
 		io.WriteString(w, r.RemoteAddr)
-	}))
+	})
+	cst := newClientServerTest(t, h2, handler, func(srv *httptest.Server) {
+		srv.Config.RegisterOnShutdown(func() { gotOnShutdown <- struct{}{} })
+	})
 	defer cst.close()
 
 	doShutdown = func() {
@@ -5251,6 +5255,11 @@ func testServerShutdown(t *testing.T, h2 bool) {
 	if err := <-shutdownRes; err != nil {
 		t.Fatalf("Shutdown: %v", err)
 	}
+	select {
+	case <-gotOnShutdown:
+	case <-time.After(5 * time.Second):
+		t.Errorf("onShutdown callback not called, RegisterOnShutdown broken?")
+	}
 
 	res, err := cst.c.Get(cst.ts.URL)
 	if err == nil {
diff --git a/src/net/http/server.go b/src/net/http/server.go
index 71f46a74f97..b60bd2481e4 100644
--- a/src/net/http/server.go
+++ b/src/net/http/server.go
@@ -2395,6 +2395,7 @@ type Server struct {
 	listeners  map[net.Listener]struct{}
 	activeConn map[*conn]struct{}
 	doneChan   chan struct{}
+	onShutdown []func()
 }
 
 func (s *Server) getDoneChan() <-chan struct{} {
@@ -2475,6 +2476,9 @@ func (srv *Server) Shutdown(ctx context.Context) error {
 	srv.mu.Lock()
 	lnerr := srv.closeListenersLocked()
 	srv.closeDoneChanLocked()
+	for _, f := range srv.onShutdown {
+		go f()
+	}
 	srv.mu.Unlock()
 
 	ticker := time.NewTicker(shutdownPollInterval)
@@ -2491,6 +2495,17 @@ func (srv *Server) Shutdown(ctx context.Context) error {
 	}
 }
 
+// RegisterOnShutdown registers a function to call on Shutdown.
+// This can be used to gracefully shutdown connections that have
+// undergone NPN/ALPN protocol upgrade or that have been hijacked.
+// This function should start protocol-specific graceful shutdown,
+// but should not wait for shutdown to complete.
+func (srv *Server) RegisterOnShutdown(f func()) {
+	srv.mu.Lock()
+	srv.onShutdown = append(srv.onShutdown, f)
+	srv.mu.Unlock()
+}
+
 // closeIdleConns closes all idle connections and reports whether the
 // server is quiescent.
 func (s *Server) closeIdleConns() bool {