diff --git a/cmd/kubeadm/app/phases/upgrade/health.go b/cmd/kubeadm/app/phases/upgrade/health.go
index 39235f5f9da..da37c6df848 100644
--- a/cmd/kubeadm/app/phases/upgrade/health.go
+++ b/cmd/kubeadm/app/phases/upgrade/health.go
@@ -64,7 +64,7 @@ func (c *healthCheck) Name() string {
 }
 
 // CheckClusterHealth makes sure:
-// - the API /healthz endpoint is healthy
+// - the cluster can accept a workload
 // - all control-plane Nodes are Ready
 // - (if static pod-hosted) that all required Static Pod manifests exist on disk
 func CheckClusterHealth(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration, ignoreChecksErrors sets.Set[string], printer output.Printer) error {
@@ -92,11 +92,18 @@ func CheckClusterHealth(client clientset.Interface, cfg *kubeadmapi.ClusterConfi
 }
 
 // createJob is a check that verifies that a Job can be created in the cluster
-func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration) (lastError error) {
+func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration) error {
 	const (
-		prefix  = "upgrade-health-check"
-		ns      = metav1.NamespaceSystem
-		timeout = 15 * time.Second
+		prefix        = "upgrade-health-check"
+		fieldSelector = "spec.unschedulable=false"
+		ns            = metav1.NamespaceSystem
+		timeout       = 15 * time.Second
+	)
+	var (
+		err, lastError error
+		ctx            = context.Background()
+		nodes          *v1.NodeList
+		listOptions    = metav1.ListOptions{Limit: 1, FieldSelector: fieldSelector}
 	)
 
 	// If client.Discovery().RESTClient() is nil, the fake client is used.
@@ -106,6 +113,25 @@ func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration)
 		return nil
 	}
 
+	// Check if there is at least one Node where a Job's Pod can schedule. If not, skip this preflight check.
+	err = wait.PollUntilContextTimeout(ctx, time.Second*1, timeout, true, func(_ context.Context) (bool, error) {
+		nodes, err = client.CoreV1().Nodes().List(context.Background(), listOptions)
+		if err != nil {
+			klog.V(2).Infof("Could not list Nodes with field selector %q: %v", fieldSelector, err)
+			lastError = err
+			return false, nil
+		}
+		return true, nil
+	})
+	if err != nil {
+		return errors.Wrap(lastError, "could not check if there is at least one Node that can schedule a test Pod")
+	}
+
+	if len(nodes.Items) == 0 {
+		klog.Warning("The preflight check \"CreateJob\" was skipped because there are no schedulable Nodes in the cluster.")
+		return nil
+	}
+
 	// Prepare Job
 	job := &batchv1.Job{
 		ObjectMeta: metav1.ObjectMeta{
@@ -114,7 +140,7 @@ func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration)
 		},
 		Spec: batchv1.JobSpec{
 			BackoffLimit:            ptr.To[int32](0),
-			TTLSecondsAfterFinished: ptr.To[int32](2),
+			TTLSecondsAfterFinished: ptr.To[int32](int32(timeout.Seconds()) + 5), // Make sure it's more than 'timeout'.
 			Template: v1.PodTemplateSpec{
 				Spec: v1.PodSpec{
 					RestartPolicy: v1.RestartPolicyNever,
@@ -141,13 +167,11 @@ func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration)
 		},
 	}
 
-	ctx := context.Background()
-
 	// Create the Job, but retry if it fails
 	klog.V(2).Infof("Creating a Job with the prefix %q in the namespace %q", prefix, ns)
 	var jobName string
-	err := wait.PollUntilContextTimeout(ctx, time.Second*1, timeout, true, func(ctx context.Context) (bool, error) {
-		createdJob, err := client.BatchV1().Jobs(ns).Create(ctx, job, metav1.CreateOptions{})
+	err = wait.PollUntilContextTimeout(ctx, time.Second*1, timeout, true, func(_ context.Context) (bool, error) {
+		createdJob, err := client.BatchV1().Jobs(ns).Create(context.Background(), job, metav1.CreateOptions{})
 		if err != nil {
 			klog.V(2).Infof("Could not create a Job with the prefix %q in the namespace %q, retrying: %v", prefix, ns, err)
 			lastError = err
@@ -162,8 +186,8 @@ func createJob(client clientset.Interface, cfg *kubeadmapi.ClusterConfiguration)
 	}
 
 	// Wait for the Job to complete
-	err = wait.PollUntilContextTimeout(ctx, time.Second*1, timeout, true, func(ctx context.Context) (bool, error) {
-		job, err := client.BatchV1().Jobs(ns).Get(ctx, jobName, metav1.GetOptions{})
+	err = wait.PollUntilContextTimeout(ctx, time.Second*1, timeout, true, func(_ context.Context) (bool, error) {
+		job, err := client.BatchV1().Jobs(ns).Get(context.Background(), jobName, metav1.GetOptions{})
 		if err != nil {
 			lastError = err
 			klog.V(2).Infof("could not get Job %q in the namespace %q, retrying: %v", jobName, ns, err)
@@ -192,7 +216,7 @@ func controlPlaneNodesReady(client clientset.Interface, _ *kubeadmapi.ClusterCon
 	selectorControlPlane := labels.SelectorFromSet(map[string]string{
 		constants.LabelNodeRoleControlPlane: "",
 	})
-	nodes, err := client.CoreV1().Nodes().List(context.TODO(), metav1.ListOptions{
+	nodes, err := client.CoreV1().Nodes().List(context.Background(), metav1.ListOptions{
 		LabelSelector: selectorControlPlane.String(),
 	})
 	if err != nil {