Auckland suburb of Albany and the building is being evacuated, reports say. Police have confirmed injuries in the area.
Emergency services say the tornado followed a straight line south from Albany before dying out near Pt Chevalier to the west of Auckland Central.
Foodstuffs has confirmed its Pak 'n Save Albany store suffered significant damage from the tornado.
The store has been evacuated and the company is still gathering information on whether staff or customers had been injured, its statement says.
Rob Crawford was on the scene when the tornado struck, where what he saw reminded him of the movie Twister.
"Carparks scattered with the remains of trees, upturned cars. There's iron off the roof of the old Placemakers, just wrapped around it ... total mini destruction within the carpark."
It's like a movie set. Is this real? Is this happening?' But when you see people lying on the ground, covered in blood, clutching their heads, it's damn real."
Samantha Davey from Albany Optometrists said it appeared that part of the roof at the neighbouring Albany Mega Centre had been torn away.
"We are a bit above the mall, looking down from our building we can see part of the mall roof is gone," she said.
"It looks like it's the bit behind Number 1 shoe Warehouse but our building is a bit above on Corinthian Drive so it's hard to tell.
"There's people at Work and Income, they said they saw a car swept up in it."
Miss Davey said the tornado passed "fairly quickly" but wasn't roaring as it may have been imagined.
One of her colleagues said her in-laws lost a few tiles of their roof in Unsworth.
Kate England was working at the Gordon Harris Art & Graphic Supplies just above the mall when the tornado hit.
"The first 10 seconds I was just in shock. It sounded like a bad car crash."
She said she watched a grey car being lifted 20 feet up in the air near the roundabout by the mall from the window of her work.
"It was the most surreal experience."
"Somebody came into the shop and said the Placemakers building, which the company moved out of about a week ago, is now just a shell."
She said the tornado came from the direction of the Westfield Mall, before moving through the Mega Centre.
In nearby Glenfield, an explosion is thought to have been heard at an electrical substation.
A resident, who did not want to be named, said a "crazy" amount of sirens could be heard in the area.
"I've never heard so many sirens in my life, and the birds have gone crazy. They just flew to the north."
It is understood that Kaipatiki Rd has been closed in Glenfield, where heavy rain is falling.
While major tornadoes are rare in New Zealand, there have been several deadly ones in recent history. 

In August 2004, Rosina Dawn Wikohika, 55, of Levin and her grandson Gary Mason, 10, were killed with a tornado struck the Taranaki town of Motunui, north of Waitara. 

On August 25, 1948, a major tornando hit the Hamilton suburb of Frankton, killing three people and damaging or destroying dozens of houses.

New Zealand tornadoes tend to be less deadly than those in other countries. More than 300 people were killed last week in a series of storms and tornadoes in the American South.