The stabbing took place at a Countdown supermarket in central Dunedin on South Island in the afternoon.
One person has been taken into custody, authorities said.
Prime Minister Jacinda Ardern said the motivation behind the attack was not clear but that there was no indication it was a domestic terror event.
Incidents of mass violence are rare in New Zealand but the country saw the 2019 Christchurch shooting when a white supremacist killed more than 50 people at two mosques.
