Six other people, including police officers, were injured and the gunman is also dead after the incident at 07:22 (19:22 GMT) on a construction site in the central business district.
PM Chris Hipkins said the attack was not being seen as an act of terrorism.
The tournament would go ahead as planned, he said.
The public, he added, could be assured police had neutralised the threat and there was no ongoing risk after the incident on Queen Street.
No political or ideological motive for the attack had been identified, the prime minister said.