The stance by the health agency has rekindled criticism the country has once again broken ranks with its neighbours and has led to some of Sweden's regions no longer providing free testing for all.
COVID-19 testing fell by 35 per cent last week compared to a month earlier.
That places Sweden in the bottom of the European Union along with countries like Germany, Spain, Poland and Finland, according to Our World in Data.
The health agency argues the resources for testing could be better used elsewhere and that there is no need to test those who are fully vaccinated as they have a low risk of getting sick and are less likely to spread the disease.
However, the timing of the decision, just as Europe is heading in to the winter season, has baffled some scientists.
One recent newspaper column said, "Sweden is once again in the dark" about the spread and ability to break disease chains.
"The number of cases is low in Sweden but considering how the outside world looks like with lots of cases in Europe, I think you should have waited with this decision," said Anders Sonnerborg, professor in clinical virology and infectious diseases at Karolinska Institutet.
"I have a hard time seeing that waiting a few months would be a major intervention in people's lives," he said.
Health Agency official Sara Byfors on Thursday defended the decision saying testing would still be at high enough level to catch trends and that testing had never caught all cases.
"If we see that the spread of infection increases and that it becomes a problem then we are prepared to reverse our decision," she told a news conference.
The number of hospitalisations and patients treated at intensive care units have started to creep up in recent weeks but are still the lowest in the European Union per capita, according to Our World in Data.
Sweden's handling of the pandemic has stood out, shunning lockdowns throughout the health crisis and instead relying on voluntary measures based on distancing and good hygiene.
The country's number of deaths per capita since the start of the pandemic is several times higher than those among Nordic neighbours but also lower than in most European countries that opted for strict lockdowns.