Mayor Andrew Little told state-owned Radio New Zealand that Wellington had received 77 millimetres of rain in less than an hour, its heaviest rainfall on record.
The deluge caused flash flooding, road closures and landslides in the city's central business district and southern suburbs.
Some people had to escape flooded homes during the night and at least one landslide hit a home.
A number of streets in the city were evacuated and the Fire and Emergency service said they responded to 150 calls for assistance overnight.
A search was under way for a man living at a property that was flooded in the suburb of Karori, New Zealand police said in a statement.
The weather had cleared for a few hours earlier on Monday, allowing some of the floodwaters to disperse, but further heavy rain was again hitting the city.
Weather forecaster MetService is warning the rain could worsen later on Monday and a state of emergency has been declared for the Wellington region.
The Wellington Region Emergency Management Office in an advisory told residents in flood-prone spots to move to higher ground for at least the next 24 hours.
An assistance centre for the region, which has a population of about 521,000, has been set up for those who need to evacuate.
New Zealand has been pounded by heavy rains in the past few days.
The Wellington region was hit by severe weather that caused flood damage overnight on Friday, while much of the northern part of the North Island was impacted by Cyclone Vaianu a week ago.
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