In Auckland, the regional public health service was following up with household contacts and other contacts as appropriate, Stuff reported.
There was a suspicion the person might have been a previously unconfirmed case from March, and that was responsible for the positive test result.
The woman said she assumed Australian authorities would have automatically alerted New Zealand health officials to her positive test.
However, after reading about the Korean traveller who tested positive to Covid-19 after returning from New Zealand to South Korea earlier this month, the woman decided to ring New Zealand's health hotline to make sure.
She discovered authorities were unaware of her case.
"I thought the countries would alert each other but it turns out they don't talk at all," the woman said.
"I was really surprised and it turned into a massive situation today that's for sure. I've spent probably four to six hours on the phone going through every step before I left."
The woman earlier notified her family and friends in the North Island and most had now returned negative results for Covid-19, although some were still waiting for their results.
The woman's family had visited her before leaving the country.
The family have been tested since hearing about the positive test result.
The woman thought her positive test result was not because she had recently contacted coronavirus but because she might have picked it up in March.
She moved to the United Kingdom in January this year, before coming home to New Zealand in March when the pandemic hit Europe.
It was just as she made it to her isolation home in Whanganui that she began to feel sick.
"I lost my sense of smell and taste and I had a bit of fatigue and fever," she said.
"You know when you start getting the flu and feel a little fatigue so that it's hard to do stuff that you normally do everyday, that's what I felt like."
She said she tried to get tested for Covid-19 twice in Whanganui, but was refused because test kits were in limited supply in March.
However, because the woman spent three weeks in self isolation and New Zealand then went into lockdown, none of her family or friends have since become sick with the virus.
The woman said she had heard from other passengers on her flight there were two other Covid-19 positive cases on the same Air NZ flight.
However, her flight had not yet been listed on the NSW Health website as having a positive case on it.
She said she now had to spend 14 nights in quarantine dating from her test on July 22.
Her case comes after the Ministry of Health confirmed to the Herald they were tracing contacts of another person who tested positive to Covid-19 in Australia after flying from Auckland to Sydney on July 6.
Kiwi health officials were alerted by authorities in Australia in that case.
They had since spoken with the passenger directly and were tracing their household and other contacts.
"At this point, it appears the person may have been a previously unconfirmed case from March and this is responsible for the positive test result," the Ministry of Health said.
"We will continue to fully investigate the circumstances of this positive result, including travel history."
It comes after a 22-year-old Korean man's recent positive Covid-19 test led local New Zealand officials to trace his movements and test close contacts.
The man had been living in New Zealand and travelled in Auckland and the South Island before leaving the country on July 21.
He subsequently tested positive to Covid-19 in South Korea.
