However, Australia's expert medical panel decided late on Sunday night to change the system.
Each Australian state will determine their own procedure for anyone who has already arrived in Australia from New Zealand and may pose a risk of transmitting the virus.
Director-General of Health, Doctor Ashley Bloomfield says he understands that people will be concerned especially around that school community, however, he wants to reassure them that they are taking this approach out of an abundance of caution.
But nearly two million residents were told on Sunday to stay at home from midnight, when the level-three lockdown begins, with schools and businesses to close except for essential services.
Auckland residents are asked to stay home whenever possible and observe social distancing rules.
The plan for a Trans-Tasman Travel Bubble allowing quarantine-free travel between Australia and New Zealand has hit another snag with Australia declaring New Zealand a "red zone" after new community transmissions were recorded in its largest city of Auckland.
At the weekend, after the three people tested positive for Covid-19, Auckland was plunged back into alert level 3 and the rest of the country moved to alert level 2.
It is not yet clear whether the lockdown will extend beyond midnight on Wednesday.
Of the three new cases, the mother looms as a likely index case, given she works at a catering company which services planes at Auckland airport.
Health officials said a mother - who works for a company providing laundry and catering services to global flights - and her daughter tested positive Saturday, before the father returned a positive sample Sunday.
The school is undergoing deep cleaning and will be closed on Monday and Tuesday as a precaution, with a testing facility to be set up on the campus.
Currently, the authorities are also carrying out contact tracing for all who have connected with the family.
Ardern has been widely praised for her management of the pandemic, with New Zealand recording just 25 deaths and less than 2,000 cases in a population of five million.
"It's a good timely reminder to everyone".
New cases are regularly caught among returning travelers, all of whom are required to spend two weeks in quarantine.
The woman and her daughter tested positive yesterday before the father returned a positive sample today.
"Remember, we have been here before".
"If you are in Auckland, please make sure that your neighbours and ensure they are looked after and supported. They stay airside but of course, it means they are using the things that go through the laundry at this individual's place of work", Ardern told Newstalk ZB.