A cruise ship is being held off the coast of New Zealand with at least one suspected case of coronavirus on board.

Three passengers on the Golden Princess have been quarantined by the ship's doctor.

One of the three has developed symptoms of Covid-19 and is being treated as a suspected case, the Canterbury District Health Board says.

The person is being tested, with the results due tomorrow.

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The ship arrived in Akaroa Harbour this morning.

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Canterbury DHB medical officer of health Dr Ramon Pink said the public health team was taking a precautionary approach.

All three passengers were in quarantine, and the cruise ship company had been very co-operative, Pink said.

"We realise this is disappointing news for other passengers and tourism/hospitality operators in Akaroa and Canterbury who were expecting to host the passengers today.

"We cannot risk the potential further spread if this person tests positive.

"Two of the three people isolated have been in contact with a confirmed case in the past 14 days."

On Saturday Prime Minister Jacinda Ardern announced all cruise ships would be banned from coming to New Zealand until June 30.

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It's not clear if the ban would have applied to the Golden Princess, which would have been en route to Akaroa when the restrictions were announced.

All 18 ships that travel under the Princess Cruises brand have been halted for two months due to the spread of Covid-19, operator Carnival announced on March 12.

Royal Caribbean Cruises has also announced today it is suspending cruising in New Zealand and Australia.

Cruises that left either country before today would continue to operate and return to Australia as planned, the company said.

PM: We can enforce self-isolation requirements

Meanwhile the Prime Minister said today that the Government and the police can enforce self-isolation if necessary.

And she says the Government's economic package, to be announced on Tuesday, will be the most significant one-off injection into the economy of her entire tenure as Prime Minister.

Yesterday Ardern announced that any person from any country, excluding the Pacific islands, is now required to self-isolate for 14 days upon arrival to the country, and she encouraged all New Zealanders to avoid all non-essential travel overseas.

As well as affecting thousands of people's travel plans, the move is expected to significantly impact Kiwis' jobs and New Zealand economy.

This morning Ardern sought to calm fears about whether people would self-isolate properly, saying that the 10,500 New Zealanders who had done it so far had been overly compliant, with some staying home for more than 14 days.

But she said authorities, including police, had the power to quarantine people at a medical facility and station staff at the door.

That power had not been used so far, she told TVNZ's Q+A this morning.

The Government has been constantly looking at global developments, and the new restrictions unveiled on Saturday were the next step to "go hard" to flatten the curve.

The goal was to avoid a large-scale community spread of the virus, and the new travel restrictions were about keeping pressure off the public health system as the number of positive cases rose.