Ms Ardern has been isolating in Wellington's Premier House, the official residence of the New Zealand prime minister, for 10 days as the virus sweeps through her family.
Her partner Clarke Gayford produced a positive test on Mother's Day, with three-year-old daughter following suit on Wednesday last week.
After seven days in isolation, Ms Ardern followed them by producing a positive test on Saturday.
"Despite best efforts, unfortunately I've joined the rest of my family," she announced on Instagram.
The Labour leader missed the announcement of New Zealand's landmark emissions reduction plan on Monday, and did not appear in parliament on Tuesday.
She will miss the budget on Thursday, and her travel on an official delegation to the United States next week is in doubt.
Ms Ardern is due to travel to the USA on Saturday on a trip which includes the Harvard Commencement address, following in the footsteps of luminaries like Winston Churchill and Oprah Winfrey.
Officials have been tight-lipped on whether COVID-19 regulations of both countries will allow her to fly and participate in planned events.
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