Metrics API Beta that Metrics Server depends on was introduced in Kubernetes 1.8.
There was no major changes in API since, thus it should work Kubernetes 1.8+ assuming that cluster fulfils
https://github.com/kubernetes-sigs/metrics-server#requirementsBefore upgrading your EKS version I would recommend some testing. Vendors like EKS can introduce cluster configuration changes that could break Metrics Server requirements mentioned above or require configuration changes.
If you cannot do upgrade testing I would recommend to use Metrics Server version v0.3.6 listed in EKS documentation
https://docs.aws.amazon.com/eks/latest/userguide/metrics-server.html as it should be most commonly used and tested.