UPDATE / Dec 7: Vector says it restored power to 700 customers overnight, leaving 635 still without power in the north-west Auckland suburbs of Whenuapai and Hobsonville remain without power.
Police said seven injured people had been taken to North Shore Hospital.
The names of three construction workers killed in the tornado would not be released as not all next of kin had been notified, police say.
Dec 6: A tornado which swept through west Auckland today has killed at least two people, unconfirmed media reports say.
Some media are reporting three people have died.
Those killed are said to have been working on a building site near Hobsonville Pt.
At least seven people in other locations have minor injuries.
MetService earlier warned more tornados could hit and issued a severe thunderstorm warning for the Auckland region and Thames/Coromandel, although this has since been lifted.
There are reports of flooding in other parts of Auckland, mainly in west Auckland.
The tornado, which struck shortly after 1pm, has brought down trees and torn roofs from houses.
Lines company Vector says people should stay away from fallen power lines and treat them as live.
Mayor Len Brown advises people to stay indoors.
Auckland Airport says all flights are affected by the storm.
Airport spokesman Richard Llewellyn says all scheduled domestic and international flights are now experiencing delays due to storm safety protocols being in place, which is restricting operations.
Some arriving flights have been diverted to other airports.
He says passengers should check the status of their flight either with their airline or the Auckland Airport website.
Why Auckland attracts tornados
Today's tornado follows another fatal one in Albany on Auckland's North Shore in May 2011.
Canterbury University meteorology lecturer Dr Marwan Katurji says the North Island, and especially the west coast, is more vulnerable to westerly and northerly winds which are associated with weather fronts.
"Warm moist air from the Tasman Sea carries within it embedded thunderstorms.
"When the air hits land it interacts with the topography to create higher wind speeds and the storms get more severe.
"The Auckland region is one of the hot spots for this activity which promotes tornados, although Taranaki is the record holder."
Dr Katurji says tornados are rare in Canterbury because it is insulated by the Southern Alps.
Victoria University geography professor Dr James Renwick says damaging tornados are associated with severe thunderstorm activity, but analysis of weather records does not show a pattern of tornado occurrences.
"These events strike at random from time to time, but they are very localised and sporadic and are not obviously tied to trends in the large-scale climate.
"At this stage, we have no indication that tornado occurrences will become more or less frequent in future."
PM gives condolences
Prime Minister John Key has expressed his condolences to the families of those who died as a result of the storm.
"This must have been an extremely frightening situation for many people in the local community.
"I'd like to thank the emergency services staff, who are responding to the situation. It's critical they are able to focus on the response.
"This extreme weather event occurred in the heart of my electorate as well as Paula Bennett's electorate.
"I have been kept informed of the situation throughout the afternoon and am continuing to receive updates," Mr Key says.