Based on @Evans Tucker's answer but uses whitelisting rather than deletion within the jq filter to only keep what we want.

kubectl get secret cure-for-covid-19 -n china -o json | jq '{apiVersion,data,kind,metadata,type} | .metadata |= {"annotations", "name"}' | kubectl apply -n rest-of-world -f -

Essentially the same thing but preserves labels.

kubectl get secret cure-for-covid-19 -n china -o json | jq '{apiVersion,data,kind,metadata,type} | .metadata |= {"annotations", "name", "labels"}' | kubectl apply -n rest-of-world -f -

kubectl get secret gitlab-registry --namespace=revsys-com --export -o yaml |\ kubectl apply --namespace=devspectrum-dev -f -

Use RBAC to authorize the serviceaccoun to use the secret on the original namespaces. But, this is not recommended to have a shared secret between namesapces.

--export is deprecated

sed is not the appropriate tool for editing YAML or JSON.

Here's an example that uses jq to delete the namespace and other metadata we don't want:

kubectl get secret cure-for-covid-19 -n china -o json | jq 'del(.metadata["namespace","creationTimestamp","resourceVersion","selfLink","uid"])' | kubectl apply -n rest-of-world -f -

They can only be referenced by pods in that same namespace. But you can just copy secret from one name space to other. Here is a example of copying localdockerreg secret from default namespace to dev:

 kubectl get secret localdockerreg --namespace=default --export -o yaml | kubectl apply --namespace=dev -f -

UPDATE

In Kubernetes v1.14 --export flag is deprecated. So, the following Command with -oyaml flag will work without a warning in forthcoming versions.

kubectl get secret localdockerreg --namespace=default -oyaml | kubectl apply --namespace=dev -f -

The accepted answer is correct, here is a hint if you are looking to copy the secret between namespaces.

kubectl get secret <secret-name> -n <source-namespace> -o yaml \
| sed s/"namespace: <source-namespace>"/"namespace: <destination-namespace>"/\
| kubectl apply -n <destination-namespace> -f -

/edit apr 2020:

Now there is a way to share or sync secret across namespaces and its by using the ClusterSecret operator:

https://github.com/zakkg3/ClusterSecret

Secrets are namespaced resources, but you can use a Kubernetes extension to replicate them. We use this to propagate credentials or certificates stored in secrets to all namespaces automatically and keep them in sync (modify the source and all copies are updated). See Kubernetes Reflector (https://github.com/EmberStack/kubernetes-reflector).

The extension allows you to automatically copy and keep in sync a secret across namespaces via annotations:

On the source secret add the annotations:

 annotations:
   reflector.v1.k8s.emberstack.com/reflection-auto-enabled: "true"

This will create a copy of the secret in all namespaces. You can limit the namespaces in which a copy is created using:

reflector.v1.k8s.emberstack.com/reflection-allowed-namespaces: "namespace-1,namespace-2,namespace-[0-9]*"

The extension supports ConfigMaps and cert-manager certificates as well. Disclainer: I am the author of the Kubernetes Reflector extension.

As answered by Innocent Anigbo, you need to have the secret in the same namespace. If you need to support that dynamicaly or avoid forgeting secret creation, it might be possible to create an initialiser for namespace object https://kubernetes.io/docs/admin/extensible-admission-controllers/ (have not done that on my own, so cant tell for sure)

Improving from @NicoKowe

One liner to copy all secrets from one namespace to another

$ for i in `kubectl get secrets | awk '{print $1}'`; do  kubectl get secret $1 -n <source-namespace> -o yaml | sed s/"namespace: <source-namespace>"/"namespace: <target-namespace>"/ | kubectl apply -n <target-namespace> -f -  ; done