On Monday, her government announced its first emissions reduction plan, a project initiated during her first term of government.

The prime minister was to videolink into the announcement while isolating but the virus laid her low, cancelling her involvement in her flagship policy and Monday's cabinet meeting.

Energy Minister Megan Woods said Ms Ardern was "doing okay" and "settling down for a week of isolation".

"We've made the decision (for her to rest as) she's got some pretty hefty obligations later in the week," she told Radio NZ.

"As she repeatedly tells everyone else, people do need to rest when they get COVID. She's really gutted not to be parliament this week, it's a pretty big week, and we're gutted not to have her there."

Ms Ardern's first brush with the virus means she will be the first prime minister in memory to be absent from parliament for a government budget, which will be handed down on Thursday.

It could also scuttle a planned trip to the United States, where the Labour leader is due to fly on Friday.

Ms Ardern has been invited to give Harvard University's commencement address next week, a major honour which has only been granted to a small clutch of world leaders.

In her absence in parliament on Monday, deputy prime minister Grant Robertson fulfilled her duties at both the climate change plan and her weekly Monday press conference.

"She will be taking it each day as it comes over the next few days and hopefully will be able to join us remotely later in the week," Mr Robertson said.

Mr Robertson - Ms Ardern's closest ally in politics - said the prime minister had provided some "affirming and positive" feedback on his performance.

"Through my own communication with her, I can assure you that she's doing OK," he said.

Ms Ardern caught COVID-19 after her partner Clarke Gayford, who tested positive on Sunday, and their daughter Neve, who did so on Wednesday.

She announced her diagnosis on Instagram, sharing a picture of a rapid antigen test as a photo.

Australian Associated Press