Of the five wounded people, three were in critical condition, one in serious condition and another in moderate condition, the St John ambulance service said in a statement to Reuters.
Witnesses told reporters outside the mall they had seen several people lying on the floor with stab wounds. Other said they heard gunshots as they ran out of the supermarket.
Prime Minister Jacinda Ardern is being briefed on the situation, a spokesperson said.
She and Police Commissioner Andrew Coster are due to address the media at 0515 GMT.
Videos posted online showed panicked shoppers running out of the mall and looking for cover as the situation unfolded.
New Zealand has been on alert for attacks since a white supremacist gunman killed 51 people at two mosques in the city of Christchurch on March 15, 2019.
In May, four people were stabbed in a supermarket in Dunedin on New Zealand's South Island.