After trying a lot of things, I found a bug report for Alpine Linux. Basically, the nslookup does not respect the server parameter, if /etc/resolv.conf has entries. Comment on that issues recommends using dig or drill for querying.2016/03/19 04:25:25 Client ip 10.0.96.1:50326 requesting /healthz probe servicing cmd sleep 10 && nslookup kubernetes.default.svc.kube.local localhost >/dev/null2016/03/19 04:25:25 Healthz probe error: Result of last exec: nslookup: can't resolve 'kubernetes.default.svc.kube.local': Name does not resolve, at 2016-03-19 04:25:23.967737423 +0000 UTC, error exit status 1
So I made a simple image and pushed it into docker hub, https://hub.docker.com/r/jyrki/arm-kubernetes-healthz-drill/. Nothing fancy, just added drill (https://github.com/jyrkiput/arm-kubernetes-healthz-drill/blob/master/Dockerfile). I used the existing image as base as I wanted to have the exechealtz available.
Then I had to change the healtz command to
drill -q kubernetes.default.svc.kube.local @localhost