The person - who is in their 60s - is in a stable and improving condition in Auckland City Hospital, Prime Minister Jacinda Ardern said.
They are a citizen of New Zealand who had been to Iran and flown back to New Zealand via Bali.
Ardern said New Zealand's pandemic plan was now being fully put into place.
"It has been through good care and good management that New Zealand has gone through such a long period of time without having a case arriving on our shores," Ardern added.
The Ministry of Health had earlier confirmed testing was underway for a suspected coronavirus case. The results of the tests were formally reported to the ministry about 4.15pm on Friday.
"I'm confident that the risk of this disease is being very well-managed," Health Minister David Clark said on Friday evening.
It was revealed the person diagnosed with the disease had tested negative for coronavirus on two previous occasions, but continued to show symptoms.
"Clinical judgment was to continue and look into greater detail," Clark said.
New Zealand was the 48th country to have a confirmed case and more sporadic cases may continue to arrive in New Zealand, Clark said.
"We are well prepared, because we've had time to be prepared."