Although Kiwis arriving home said they accepted the self-isolation rules as a necessary inconvenience, a number of European backpackers told her that though they will try to keep their distance from people as they travel in a campervan, they planned on travelling around the country as normal.

"It's actually these people who are the biggest risk in terms of coronavirus on our soil because these people have been travelling far and wide - so it's anyone's guess how the New Zealand authorities are going to keep track of travellers like these," Speedy told The Am Show.

Prime Minister Jacinda Ardern said any foreign travellers who fail to self-isolate could be deported.

"We have the ability to quarantine them - put them in a facility, quarantine them, have a police officer stand outside the door and make sure they don't leave. But I've also asked the question whether I have the power to deport as well," Ardern told The AM Show on Monday.

One traveller Newshub spoke to said it will be a long 14 days in isolation.

"I do have annual leave, [but] I don't know if I have any of that left and I do have the odd sick day so hopefully I have a bit of money there - otherwise I'm just going to have to wear it for two weeks," said Sally Michael, who also arrived in Christchurch from Australia.

The stricter travel restrictions will be reviewed in 16 days.

Also affected are cruise ships, which have been banned from entering the country until at least June 30.

Cargo ships and essential flights carrying items such as pharmaceuticals will not be affected, with Ardern insisting the new measures were "about restricting the movement of people, not products".

"We will continue to have imports come into New Zealand," Ardern said on Saturday.

Queenstown's Mayor calls for calm

In Queenstown, the city's Mayor is urging residents to remain calm, after the region's first case of COVID-19 was confirmed over the weekend when a Danish woman tested positive.

"It's a woman travelling with her partner and children staying in a campervan," Mayor Jim Boult told Newshub.

He says the woman was initially hospitalised and is now in self-isolation.

Contact tracing is currently underway, he said.

"Clearly, the authorities have acted to handle it very appropriately."

Boult says he hopes there won't be a knee-jerk reaction in the region following the case.

"When a case was first discovered further north there was some panic-buying which proved totally unnecessary and I really hope people don't do that."

Cruise ship passenger tests negative

Earlier on Monday, another suspected case in the South Island - this one on a cruise ship berthed off Akaroa - came back negative.

The passenger on board the Golden Princess was ordered into self-isolation by the ship's doctor after showing symptoms of COVID-19.

But according to TVNZ, which cited the cruise ship's owners, test results came back negative and now all passengers on board the ship have been given to all-clear to disembark.

There have been more than 156,000 cases of COVID-19 confirmed around the world so far, with the death toll standing at almost 6000.

In New Zealand, all eight confirmed cases of the virus have been related to people arriving from overseas.

As of yet, there have been no recorded cases of human-to-human transmission.