Social Democrat Andersson, 54, attended a debate in parliament on Wednesday, after which two other party leaders - Annie Loof of the Centre Party and Per Bolund of the Greens - also tested positive.
Sweden's king, queen and crown princess were all hit with coronavirus infections in early January.
Andersson "is following the current recommendations and will perform her duties from home. The PM is feeling well, given the situation," her spokesperson said.
The country of 10.4 million has repeatedly set new daily records for COVID cases this month as the highly infectious Omicron variant takes hold, registering 25,567 cases on Thursday, just shy the previous day's all-time high.
That has raised pressure on the health service, forced the government to reintroduce curbs and overwhelmed the testing system in many regions.
The proportion of positive tests has sky-rocketed to 32% of all tests this week after having been under 10% for almost all of the pandemic, the health agency said on Thursday.
The agency expects daily cases to peak later this month at almost 70,000.
Around 1,200 patients with COVID are currently being treated in hospitals, with around 100 in intensive care.
(Reporting by Niklas Pollard, Simon Johnson and Johan Ahlander; editing by John Stonestreet)
