The news comes as Cabinet are deciding whether to lift Auckland out of the level 3 lockdown and the rest of the country out of level 2.
Prime Minister Jacinda Ardern is expected to make the announcement at 4.30pm.
The lockdown has seen businesses unable to operate and most school children stuck at home.
Authorities are yet to discover how the family of three became infected with the virus, and until that's been established there remains a possibility that there are undetected cases of Covid-19 circulating in the community.
Photo RNZ Caption: New Zealand’s Covid-19 Response Minister Chris Hipkins