The man, in his 60s, arrived from Melbourne on 13 June on Air NZ flight 124 and started showing signs of illness two days later while in quarantine. Yesterday, the Ministry of Health said he had tested positive.
Former RNZ reporter Alexa Cook is in quarantine at the Novotel Auckland Airport, having arrived from the UK.
She is concerned after learning she was on the same flight as the man.
"There was no social distancing. We were sat in the middle of a row of four people - we had people right up against us," she said.
"Masks were not compulsory, the flight attendants were only wearing a mask and no other PPE ... and the flight itself seemed to be very crammed, very busy."
And yesterday Director-General of Health Dr Ashley Bloomfield said masks will be compulsory for every passenger on board flights from Australia, for the duration of the flight.
At the moment it is not compulsory to wear masks on incoming flights.
Air NZ told RNZ yesterday it was not treating the masks as compulsory but that they would be offered to passengers on trans-Tasman flights.
Alexa Cook was tested for Covid-19 yesterday and is expecting to get the results on Saturday.
"We finally got tested [yesterday, which is] day five. We were told we'd be tested on day three and day 12 as per those new regulations that came in last week," she said.
"We had to ask a few times, 'When's our test going to be? Can we please get tested?' Because I wanted that peace of mind before going back to my family."
The Government bolstered its quarantine procedures after two women were allowed to leave quarantine without being tested and later were found to be infected.
"But the facility was being managed very strictly to start with," she said.
She was astounded by the news that the women had been able to leave quarantine without being tested having arrived from the UK - a Covid-19 hotspot.
"From the experience we've been going through, that these facilities, at least the one we're in certainly, is really strict.
"I'm really surprised that we go through all of this effort with the quarantining and the managed isolation and the testing just to hear that people have been let out without those test results. That seems to be, to me, absolute madness."