"We are continuing to take tests again and again, but it hasn't succeeded," according to head microbiologist Mia Brytting at SMI to news agency TT.
Further tests would take several days, a statement from the Swedish Institute for Infectious Disease Control (Smittskyddsinstitutet, SMI) said.
"Only then will we be able to confirm or rule out with certainty whether this is a case of the new influenza" known as swine flu or A(H1N1), it added.
The sample, from a women in the Stockholm area, was an A-type flu virus that was not any of the usual ones circulating this season, said the institute.
The person was a woman in her 50s recently returned from a trip to the United States, said a statement on the website of the Stockholm county infectious disease unit.
"The woman ... had a short and mild illness and is now healthy," SMI said.
"People close to her are being treated for preventive purposes with anti-viral drugs."
Neither she nor her family had required hospital care, nor been placed in quarantine, infectious diseases doctor Bo Svenungsson told Swedish news agency TT.
"She is no longer infectious. She does not need to stay at home" he said.
If tests confirmed that the woman was indeed infected with swine flu, it would be Sweden's first case of the illness.