The outbreak in NZ's biggest city has led NZ Cricket to move the three final games of the series to Wellington's Sky Stadium.

Clashes on Wednesday, Friday and Sunday to conclude the five-match T20 series will be played behind closed doors. New Zealand lead the series 2-0.

As players enjoyed a weekend off, four players - Martin Guptill, Mark Chapman, Jimmy Neesham and Glenn Phillips - travelled to Auckland to be with their families for the break.

None have travelled to regions where positive cases have been identified, none have symptoms and each player left Auckland as soon as they could following the lockdown announcement.

Still, the Black Caps ordered the four be tested on Sunday and confined them to their hotel rooms on Monday as they await the result.

The government's advice for members of the public who have not come into contact with the virus is to only get tested if you are symptomatic.

The players will also miss training on Tuesday if the test results are not back.

Batsman Devon Conway said the move was "sensible".

"They're doing their thing to make sure everyone's safe. I'm sure we'll see them at training tomorrow," he said.

"Yesterday we got summoned to go to the hotel and stay in a small bubble together to create that secure environment for ourselves.

"It's a smart move to ensure we're playing our part."

While Auckland is at alert-level three, the rest of the country is at alert-level two, which allows regular movement of people, but limits gathering sizes.

"We'll be in and around the hotel as much as possible to try and be careful," Conway said.

"We'll be spending a lot of time in our rooms watching TV and playing games."

Australian Associated Press