The breach was found during routine passenger checks after the man arrived in New Zealand on Monday. The passenger is now in Northland, self-isolating.
"Immigration New Zealand has a role to play in ordinarily screening passengers who are travelling to New Zealand," Immigration NZ manager Peter Elms said.
"As part of the wider government's efforts Immigration has been involved in screening passengers as part of the quarantine-free travel, and it was those screening exercises that picked up this individual and notified the Ministry of Health.
"This gentleman had travel booked from Perth to Sydney and then onwards to New Zealand.
"During the course of the weekend the latter part of that travel leg was cancelled – the flight from Sydney to Auckland was cancelled. Then what happened was the individual sought to book an alternative flight with a different airline and took another flight from Sydney to Auckland.
"They left Perth during the lockdown. The first time we became aware we had an individual who had potentially breached the eligibility requirements was when he arrived in Auckland.
"As soon as we became aware of that we took steps to notify the Ministry of Health and put the response into effect," Elms said.
"He had left the airport by the time we realised that that was a passenger that had come from Perth and was ineligible.
Elms said there was a reliance on people's honesty.
"We don't have visibility of all of the traveller movements in Australia ... traveller movements in Australia are on airline records. Immigration and other border agencies have some access to advanced passenger information, and we use that information to try and manage the risks associated with people movements.
"But let's remember, we're in a quarantine-free travel environment, the normal risks that Immigration would manage would not extend to New Zealand systems and they would not extend to people breaching quarantine-free travel.
"They've got to be honest with their declarations they make, both to the airline and to border agencies.
"We also rely on airline systems. So airlines have a criteria and protocols they go through to check the eligibility of passengers.
"In the background we have border systems that are operating that take the passenger information and use that to try and detect ineligible passengers.
"Over the weekend, Immigration passenger screening systems identified over 70 people who were traveling from Perth into domestic airports in Australia, and then connecting with onward travel to New Zealand.
"Immigration, in conjunction with airlines and other border agencies, successfully intervened and managed to the risks of those people."
Elms said the man now in Northland was the only one who made it to New Zealand.
"There were particular aspects related to this individual's case, which made it extremely difficult to pick him up before he boarded the plane," he said.
"There were deliberate changes made to the travel itinerary and the travel booking that made it extremely difficult for border agency staff to pick up that individual's details prior to arriving in New Zealand.
"There was enough information known to give a good indication that the person knew that he should not be travelling to New Zealand. Indeed, his flight to New Zealand had been cancelled."
The question of penalties for the individual was for the Ministry of Health and NZ Police to answer, Elms said.
"It would be potentially a breach of the Air Border Order, and there are penalties associated with that."
The ministry this afternoon said the public health safety risk was assessed as low.
It specifically noted in a statement that any person who was ineligible for quarantine-free travel was required to isolate for 14 days, "and is subject to penalties".