It touched down around 1500 (0300 GMT) in the city's Albany area and then moved south, felling trees and tearing roofs off houses.
Cars were overturned by the tornado, which left a 5 km-long (3 mile-long) trail of damage.
A roof was also ripped off a shopping centre in Albany, local media said.
Auckland Mayor Len Brown said that the death toll could rise. "We've had two confirmed fatalities, it's absolutely disastrous," he told local media.
Witnesses described debris flying though the air and cars torn from the ground as the slow-moving funnel passed.
"There's probably six or seven seriously damaged cars, and I saw cars flying off the ground about 30 meters (100 feet) in the air," shop owner Hamish Blair told the Associated Press news agency.
New Zealand's Stuff news website said that at least 18 people had been taken to hospital.
Police warned local residents to stay inside until the weather settled.
Let me take the stars down from the sky
Let me take the faith from your foundation
Let me take the wrong to make it right
Let me take away the dark like I’ve been here all night
Ending before I begin
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