diff --git a/staging/src/k8s.io/apiserver/pkg/server/genericapiserver.go b/staging/src/k8s.io/apiserver/pkg/server/genericapiserver.go
index 0b36aab67f95a..e2f462b30b419 100644
--- a/staging/src/k8s.io/apiserver/pkg/server/genericapiserver.go
+++ b/staging/src/k8s.io/apiserver/pkg/server/genericapiserver.go
@@ -326,6 +326,11 @@ func (s preparedGenericAPIServer) Run(stopCh <-chan struct{}) error {
 		defer close(delayedStopCh)
 		<-stopCh
 
+		// As soon as shutdown is initiated, /readyz should start returning failure.
+		// This gives the load balancer a window defined by ShutdownDelayDuration to detect that /readyz is red
+		// and stop sending traffic to this server.
+		close(s.readinessStopCh)
+
 		s.Eventf(corev1.EventTypeNormal, "TerminationStart", "Received signal to terminate, becoming unready, but keeping serving")
 
 		time.Sleep(s.ShutdownDelayDuration)
@@ -396,7 +401,6 @@ func (s preparedGenericAPIServer) NonBlockingRun(stopCh <-chan struct{}) error {
 	// ensure cleanup.
 	go func() {
 		<-stopCh
-		close(s.readinessStopCh)
 		close(internalStopCh)
 		if stoppedCh != nil {
 			<-stoppedCh