Prime Minister Jacinda Ardern has announced Auckland will go into level 3 lockdown, and the rest of the country will go into level 2.
People should prepare themselves for the possibility restrictions will stay in longer than three days, scientists say.
Auckland moves to level 3 at noon today for three days, until midnight on Friday, after news of a community outbreak of Covid-19 - the first in more than 100 days.
Four membersof a South Auckland family have tested positive and health authorities are racing to find the source.
Everyone working at the border or in managed isolation will be swabbed and there will be mass testing across the city. Two pop-up centres are opening this morning in Ōtara and New Lynn.
The rest of New Zealand is entering alert level 2 from midday today for three days, also until midnight on Friday.
However, Professor Shaun Hendy, a physicist from Auckland University, said people should prepare themselves for the possibility restrictions will stay in longer than three days.
"This initial period is to try to give us a handle on how big the outbreak might be," he told Morning Report.
"We haven't identified the links or the chain of transmission back to the border, which is the most likely route of entry for these new cases.
"If we can identify that, then that possibly gives us the chance of a more localised and shorter lockdown.
"If we're unable to do that people should be preparing themselves for a longer lockdown period."
Over the long term it was not possible to keep Covid-19 out, he said. "This is sooner than we would have hoped but we have been preparing for it."
Hendy said there was a likelihood it has got out of Auckland as someone in the chain of transmission could have travelled outside the area.
"I think people around the country should act as if the disease is present in the community."
Microbiologist Siouxsie Wiles said because the source of the four new Covid-19 cases have not yet not been located, cases could appear in other parts of the country.
"That's why the next few days are absolutely crucial, to understand how far this outbreak might have alread spread," she told Morning Report.
Wiles said New Zealand had acted fast and hard, whereas in Melbourne, which went from a handful of cases to thousands, it took five weeks to enact this kind of lockdown.
"It may well be if we start to see cases in the rest of the country that we all move up a level.
"So everybody must be prepared that this will last longer than three days."
She said the important thing for everyone in the parts of the country at level 2 was physical distancing and wearing masks.
Otago University public health professor Michael Baker said the best scenario was that further investigation found links to an overseas source and that the outbreak is small and quickly controlled.
"It's always been a high risk that we would see more cases in New Zealand because we have a lot of people coming back into New Zealand.
"New Zealanders need to be able to return to this country but it does pose this risk."
The priority was to control the outbreak, and then to work out what allowed this to happen, he said.
"We've got very good techniques for understanding these outbreaks and there's genomic methods that can link these cases to potential cases detected in managed isolation or quarantine facilities."
