The couple are in their 20s and arrived from India on a repatriation flight from Delhi on June 5.
They also have an infant, who has not been tested because of the child's age.
Director general of health Dr Ashley Bloomfield says it is still to be determined if the child is a probable case. If the child is not tested, this would be done by looking at their symptoms.
The couple did not show any symptoms of Covid-19 and were picked up in health and welfare checks that are conducted every day, Bloomfield said.
They were tested on Thursday in Auckland as part of the day-12 swabbing process.
An interview with the couple today "may uncover a little bit more about where this couple are at in terms of the cycle of infection," Bloomfield said.
"It may well be that they had the infection and it had passed before they left India, and that these are late positive results ... we have seen this before in cases in New Zealand."
The couple have been transported from the Grand Millennium Hotel - where they had been staying - to the Jet Park Hotel in Auckland.
They will be clinically monitored from today.
Everyone at the Grand Millennium Hotel would now be tested, Bloomfield said.
By the end of today, Bloomfield says they expect to confirm they have tested everyone from the flight the couple were on.
The flight number was AI1306 - an Air India flight.
All the passengers on this flight, and who had stayed with the couple at the Grand Millennium Hotel, will have entered a managed isolation facility as well.
It was one of several flights MFAT organised during the past few months.
A Ministry of Health staff member is now going to look at CCTV footage from the Grand Millennium Hotel "especially over this last day or two" to check if there is any other contact with others of which the ministry is unaware.
Other people being isolated there will be prevented from leaving at least until today's case interviews are completed.
"We have paused anyone leaving this facility, even those who have had a test and returned negative, just until we've done the case interview and just checked there's been no potential interaction between others and this couple that could have any risk."
Bloomfield said he was confident all procedures were followed correctly in detecting the positive results announced today.
Yesterday, 7707 tests for Covid-19 were undertaken nationally.
Bloomfield provided today's update at a press conference in Wellington at 1pm.
He said New Zealand was in the fortunate situation of having had so few cases that those that were discovered received "a lot of attention".
He said the reason we were seeing more cases this week - after several weeks of no cases - was because "we are seeing an increasing number of Kiwis returning from around the globe".
"Just to reiterate the point that I have made, there is still a global pandemic raging, and just last night the director general of the World Health Organisation noted that the global pandemic is accelerating," Bloomfield said.
"There is an increased likelihood we will see Kiwis coming back especially from countries where there is a higher rate of infection, like India," Bloomfield said.
"This explains why we are now detecting these cases at the border.
"I do want to reiterate there is not now, nor has their ever been, stigma around Covid-19.
"It is a virus that does not discriminate and we have seen world leaders and senior public health and medical people around the globe be infected with this virus.
"Please remember it could be your relative, mother, brother or sister or father. Or it could be a friend who has returned home and is sitting in a hotel room with a positive result for the virus.
"Please be compassionate and kind. We are all in this together."
Bloomfield said "it is not new" that the Stanford Hotel in Auckland had busloads of people being transported to it this week, because it had been used as a managed isolation facility "for some time".
There are 15 managed isolation facilities in Auckland and Christchurch.
Bloomfield said there had been no further infections of Covid-19 in the managed isolation facilities since the beginning of April "either within the facilities, or once they've left the facilities".
He said there had been some "surveillance testing of staff" in isolation facilities during May and no infections were uncovered there.
"We haven't seen any further spread within facilities as a result of the nearly 40 cases we have dealt with in managed isolation."
Before this week, New Zealand had 35 cases of Covid-19 identified among people returning into managed isolation. Anyone who was symptomatic for Covid-19 when they arrived - or who developed symptoms - was managed in New Zealand's dedicated quarantine facilities.
Today's two cases were asymptomatic, and this demonstrated the managed isolation system was "working as demonstrated", Bloomfield said.
Today's update follows a spike on Thursday of 6273 tests, including many people currently or previously in managed isolation and who may have been contacts of recent cases.
After a run of 24 days with no new cases, two sisters were confirmed on Tuesday as confirmed cases after recently arriving from Britain.
A man who flew from Pakistan was confirmed as the third new case on Thursday and is in quarantine.
The sisters had been released from managed isolation in Auckland without a test on a compassionate exemption immediately after their mother died, and drove to Wellington where they tested positive.
They had 401 contacts - including airline passengers - of which 174 had returned a negative result by yesterday, but with most test results still pending.
Bloomfield has been under pressure in the past week after the case of the sisters revealed that the testing regime in place from June 9 had not been working properly.
Those who arrive at the border with symptoms are taken to a quarantine facility and tested.
Other arrivals are also isolated for 14 days and from June 9 were supposed to have been tested at about day 3 and day 12.
Bloomfield said yesterday that, between June 9 and June 16, 55 people in managed isolation had been granted compassionate exemptions to leave early.
Bloomfield today said the Ministry of Health had made sure everyone who had left a managed isolation facility since June 9 had been tested for Covid-19 either before they left or since.
More than 2000 of those people had had a test result, Bloomfield said.
They had all been negative, but a few hundred results were pending.
Bloomfield said he did not know how many people were still in quarantine hotels as of today, but the numbers would be included in a media release later today.
Bloomfield says he doesn't know exactly how many managed isolation facilities are shared by members of the public not isolating for Covid-19, but he will provide the number.
"There are a number that are," Bloomfield said.
"The issue here is about ensuring that people are completely separated and that the procedures in place are really good and that infection prevention control procedures are excellent.
"Remember we now have several months of experience. The extent which those processes are put in place in those facilities is quite remarkable including the physical distancing, the way meals are delivered, the way people are processed as they come in.
"Fleeting interaction or going past people is not a risk of infecting someone else. And you can take a photo which may show people passing each other. That doesn't mean there's a risk."
Bloomfield said they are planning to audit all the procedures at isolation facilities "to make sure they are rock solid".
"It also takes the full cooperation of the people in the facilities to make sure they are abiding by what the expectations are," he said.