The woman was admitted on Friday to Vrinnevi Hospital's infectious diseases ward, where she was being treated for pneumonia.
Test results released on Saturday showed that she had also contracted the A/H1N1 virus.
She died at the hospital on Monday.
The 20-year-old was the first woman in Sweden to die from an illness directly linked to the swine flu.
Previously middle-aged men made up the eight first victims in Sweden whose deaths from swine flu-related illnesses have been confirmed by the authorities.
Local health authorities are set to hold a press conference dealing with the young woman's death at 1pm on Wednesday.