That will be reviewed in 24 hours.
Ardern said the government expects to start offering the vaccine to border and managed isolation facility workers on February 20.
She said this was the "right thing to do".
It was also a positive that all three cases were in the same family and not in the community.
She said the Government is asking Aucklanders to "stay home".
That will help stop the spread, she said.
"There's been a huge amount of work around these cases already today and there will be people in the public health response and elsewhere working into the night".
Papatoetoe High School's doors will stay shut for tomorrow and Tuesday as a precaution while the Ministry of Health investigates the source of infection.
"It would be on many people's minds, there is a spectrum and this definitely includes the more worrying possibility of community outbreak where we don't really know the extent of it".
Public venues, such as pools and playgrounds, will be closed.
People board a bus in Auckland. "It's now up to everyone to keep scanning in with the NZ COVID Tracer app, stay home and get tested if you feel sick, and follow good hygiene practices".
For the rest of New Zealand, schools remain open.
She said NZers had enjoyed more freedoms than anywhere else in the world.
The outbreak marks the first new cases outside of quarantine in nearly three weeks.
The PM, health officials and other ministers used to do this when New Zealand was at higher alert levels.
New Zealand's Prime Minister Jacinda Ardern has announced that Auckland will be locked down for three days after three positive Covid tests were announced on Sunday.
Officials are in the process of figuring out if the family - who are moving to the Jet Park MIQ facility - has infected anyone else. She will not be attending the Big Gay Out this afternoon.
Hipkins said border workers would be vaccinated at their workplaces and their household contacts would be asked to go to a dedicated place to get their jabs.
"There is a number of gaps in our knowledge around these cases".
New Zealand has said it secured up to 750,000 courses of the Pfizer COVID-19 vaccine through an Advance Purchase Agreement, and was seeking a further small allocation through the COVAX Facility.
It said: "Whole genome sequencing is being rapidly carried out so we can learn whether these infections are one of the more transmissible variants reported overseas, which we've also detected around other border-related cases in New Zealand recently".