Queensland Health says the first person in Australia who tested positive for swine flu is free to return home to Sydney.

The 28-year-old woman yesterday received a "weak positive" result after flying into Brisbane from Los Angeles on Thursday.

She had flu-like symptoms in the United States about 10 days before flying to Australia.

On arrival she went to her parents' home in Brisbane, but is now free to go anywhere.

Federal Health Minister Nicola Roxon said the woman had fully recovered by the time she returned to Australia.

"We have a person who had contracted the disease overseas and has fully recovered by the time they returned to Australia," she said.

Meanwhile Queensland Health says it has left phone messages for two Queenslanders who were on a flight with the woman confirmed to have swine flu.

The Queenslanders are part of a group of 19 passengers on the flight that are still being traced.

The 10 other Queenslanders have been contacted.

The other seven people are being contacted by their state health authorities.