The two pods are stranded at the southern end of Mason Bay, approximately two kilometres apart.
Doc say half of the whales have had to be euthanised due to their condition, and the remote area they were found.
The other half had already died.
They say the likelihood of being able to successfully re-float the remaining whales was extremely low, so the most humane thing to do was to euthanise.
Doc has notified local Ngai Tahu iwi and they're working together on next steps.
A number of strandings occurred on New Zealand shores over the weekend, but the events are unlikely to be related.