Director-General of Health Dr Ashley Bloomfield said the couple returned to New Zealand on a repatriation flight from Delhi - AI-1306 - and arrived on 5 June. They also have an infant who has not been tested due to age.
The couple showed no symptoms and returned a positive result after being tested on day 12 of isolation.
"This morning the couple and their child have been transferred from the hotel where they have been, the Grand Millenium, to the Jet Park quarantine hotel."
People at the Grand Millennium Hotel are being tested, as well as people who were on the same flight. Dr Bloomfield said they should all be tested by the end of the day.
The couple's minimum 14-day isolation period starts from today.
Dr Bloomfield said the country was now getting cases - after a streak of several days of no cases - because more New Zealanders were returning, while at the same time the number of cases overseas continued to grow.
He said the cases demonstrated that the system of testing incoming people at day three and 12 was working.
There are now five active cases in New Zealand, after two positive test results on Tuesday and one new case on Thursday.
On Tuesday it was revealed that two women who had arrived from the UK had tested positive after they were released from isolation on compassionate grounds.
Thursday's positive case was a man in his 60s who is in quarantine after arriving from Pakistan.
Dr Bloomfield reiterated that there should be no stigma attached for people who have had the virus. He said it had been caught by world leaders and doctors, and could affect your parents, grandparents, children or siblings.
"Please be compassionate and kind."
Speaking about the case of one man who apparently was taken from one facility to the airport for transfer but instead was taken back to another managed isolation facility: "As long as the procedures are appropriate, it's perfectly safe ... everyone is being tested and no one is leaving the facility."
He said anyone who was allowed to leave managed isolation under compassionate exemptions - which were now temporarily suspended - had now been tested.
Another group who was in Auckland is being flown down to Christchurch today because of insufficient capacity in Auckland, Dr Bloomfield said.
He said there had been some catch-up testing in the past few days of people who should have been tested and had not been, and extra people with appropriate PPE had been deployed to perform the swabs.
He said there were about 2400 people who had left a managed isolation facility but had not had a test, they were now being followed up with, and have either been tested or are being tested.