Health officials said a 56-year-old woman who had recently returned from Europe tested positive days after completing a compulsory two-week period of managed isolation.
Contact tracing efforts are under way, and authorities have published a list of locations the woman visited.
New Zealand has been widely praised for its response to the pandemic.
The country, with a population of five million, has recorded 1,927 confirmed cases and 25 deaths over the course of the pandemic.
The Ministry of Health said the woman had tested negative twice before leaving an isolation facility in Auckland on 13 January.
She started developing mild symptoms two days later, which then got progressively worse. She received a positive test result on Saturday and has been isolating at home.
In a press conference on Sunday, Health Minister Chris Hipkins said it was too soon to speculate on the "origin or the strain of the infection".
But the ministry said it was "working on the assumption any case might be a more transmissible variant and [was] taking appropriate precautions".
Mr Hipkins said it was "too early" to comment on any further response.
The woman visited a number of places in New Zealand's Northland region after leaving isolation.
The Health Ministry published a list of the locations, including supermarkets, restaurants and a gallery.
They said anyone who was at these places at the same time was considered a "casual contact", and asked them to stay at home and get tested "out of an abundance of caution".
Four close contacts of the women have also been tested and are isolating.