At least four other people are thought to have been injured and the gunman is also dead after the incident which came at 07:22 (19:22 GMT).
Mayor Wayne Brown said it was a “dreadful thing to happen” in his city.
The shooting happened hours before the city is due to host the Fifa Women’s World Cup opening match.
All Fifa personnel and football teams are safe and have been accounted for, the mayor said.
Police say the incident on Queen Street has been contained.
Earlier, the mayor warned people should stay home and avoid travelling into the city.
The opening match is to be held between New Zealand and Norway in the city’s Eden Park.
Biggest Women’s World Cup set to get under way
Police say they heard reports of a person discharging a firearm inside the construction site, and the gunman moved through the building and continued to fire.
The man then went into a lift shaft and police attempted to engage with him.
Further shots were fired by the man and he was found dead a short time later, police say.
They add that the incident is not viewed as a national security risk.
BBC
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