Her daughter Neve tested positive on Wednesday, she added in the post. Her partner Clarke Gayford tested positive on Sunday.
"Despite best efforts, unfortunately I've joined the rest of my family and tested positive for Covid-19," Ardern wrote on social media.
Ardern has been symptomatic since Friday night, according to a statement, and has "moderate" symptoms. She returned a weak positive Friday night and a clear positive this morning on a RAT test.
Ardern will be required to isolate until the morning of Saturday 21 May.
Ardern, who has been isolating since Gayford tested positive, will now have to miss the Budget announcement on Thursday and the release of the government's Emissions Reduction Plan on Monday.
"There are so many important things happening for the government this week," she wrote.
"I'm gutted to miss being there in person, but will be staying in close touch with the team and sharing some reckons from here.
"To anyone else out there isolating or dealing with Covid, I hope you take good care of yourselves!"
Ardern's upcoming travel to the United States, scheduled for late May, will go ahead as planned at this stage.
Deputy Prime Minister Grant Robertson will take the post-cabinet press conference on Monday.