The man and woman were found “deceased” on Thursday morning at the property in West Auckland.
“We can confirm post-mortem results indicate injuries consistent with an animal attack,” police said in a statement.
The ram was in the same paddock where the bodies were discovered.
One other unidentified person suffered a minor injury after being attacked by the ram — a male sheep — in the enclosure, police said.
“Once our staff arrived at the scene they too were confronted and approached by the ram,” police added.
“On undertaking a risk assessment, the ram was shot and died at the scene.”
Police confirmed one of their officers had killed the agitated animal.
The couple’s nephew Dean Burrell said the victims were in their 80s and had died in a “tragic accident” involving the animal, according to local media outlet Stuff.
New Zealand is home to five million people and about 25 million sheep.