[FLINK-35402][helm] Add labels to metadata

diff --git a/docs/content.zh/docs/operations/helm.md b/docs/content.zh/docs/operations/helm.md
index 12425a1..54adfde 100644
--- a/docs/content.zh/docs/operations/helm.md
+++ b/docs/content.zh/docs/operations/helm.md
@@ -76,7 +76,7 @@
 | rbac.create                                    | Whether to enable RBAC to create for said namespaces.                                                                                                          | true                                                                                                                                                                                                                                                                                           |
 | rbac.nodesRule.create                          | Whether to add RBAC rule to list nodes which is needed for rest-service exposed as NodePort type.                                                              | false                                                                                                                                                                                                                                                                                          |
 | operatorPod.annotations                        | Custom annotations to be added to the operator pod (but not the deployment).                                                                                   |                                                                                                                                                                                                                                                                                                |
-| operatorPod.labels                             | Custom labels to be added to the operator pod (but not the deployment).                                                                                        |                                                                                                                                                                                                                                                                                                |
+| operatorPod.labels                             | Custom labels to be added to the operator pod and deployment.                                                                                        |                                                                                                                                                                                                                                                                                                |
 | operatorPod.env                                | Custom env to be added to the operator pod.                                                                                                                    |                                                                                                                                                                                                                                                                                                |
 | operatorPod.envFrom                            | Custom envFrom settings to be added to the operator pod.                                                                                                       |                                                                                                                                                                                                                                                                                                |
 | operatorPod.dnsPolicy                          | DNS policy to be used by the operator pod.                                                                                                                     |                                                                                                                                                                                                                                                                                                |
diff --git a/docs/content/docs/operations/helm.md b/docs/content/docs/operations/helm.md
index 12425a1..54adfde 100644
--- a/docs/content/docs/operations/helm.md
+++ b/docs/content/docs/operations/helm.md
@@ -76,7 +76,7 @@
 | rbac.create                                    | Whether to enable RBAC to create for said namespaces.                                                                                                          | true                                                                                                                                                                                                                                                                                           |
 | rbac.nodesRule.create                          | Whether to add RBAC rule to list nodes which is needed for rest-service exposed as NodePort type.                                                              | false                                                                                                                                                                                                                                                                                          |
 | operatorPod.annotations                        | Custom annotations to be added to the operator pod (but not the deployment).                                                                                   |                                                                                                                                                                                                                                                                                                |
-| operatorPod.labels                             | Custom labels to be added to the operator pod (but not the deployment).                                                                                        |                                                                                                                                                                                                                                                                                                |
+| operatorPod.labels                             | Custom labels to be added to the operator pod and deployment.                                                                                        |                                                                                                                                                                                                                                                                                                |
 | operatorPod.env                                | Custom env to be added to the operator pod.                                                                                                                    |                                                                                                                                                                                                                                                                                                |
 | operatorPod.envFrom                            | Custom envFrom settings to be added to the operator pod.                                                                                                       |                                                                                                                                                                                                                                                                                                |
 | operatorPod.dnsPolicy                          | DNS policy to be used by the operator pod.                                                                                                                     |                                                                                                                                                                                                                                                                                                |
diff --git a/helm/flink-kubernetes-operator/templates/flink-operator.yaml b/helm/flink-kubernetes-operator/templates/flink-operator.yaml
index 69e1f8f..87a3e80 100644
--- a/helm/flink-kubernetes-operator/templates/flink-operator.yaml
+++ b/helm/flink-kubernetes-operator/templates/flink-operator.yaml
@@ -23,6 +23,11 @@
   namespace: {{ .Release.Namespace }}
   labels:
     {{- include "flink-operator.labels" . | nindent 4 }}
+    {{- if index (.Values.operatorPod) "labels" }}
+      {{- with .Values.operatorPod.labels }}
+        {{- toYaml . | nindent 4 }}
+      {{- end }}
+    {{- end }}
 spec:
   replicas: {{ .Values.replicas }}
   strategy: