The woman, who travelled on a flight with 15 other people, landed in Perth on Tuesday, September 21.
As the woman was from an "extreme risk" jurisdiction, she was taken to hotel quarantine and given a COVID-19 test before being returned to NSW.
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She returned a positive result and will undertake the full 14 days of quarantine in Perth as police consider further action.
Premier Mark McGowan said there was no cause for concern to the community.
All the woman's close contacts in WA – her flight-mates – are in hotel quarantine, and have all returned a negative test result.
Mr McGowan said he "didn't know" how the invalid NSW arrival who tested positive to COVID-19 in Perth had made the trip.
Despite not having a valid G2G pass, Mr McGowan said, she was able to board a Virgin flight.
"How, I don't know, as they're not supposed to let her," he said.
He said he believed the woman was originally from Western Australia and seeking to return home, but her application had been rejected as she was travelling from an "extreme risk" category.
Mr McGowan said the good news was that it proved the border security system was working.
"We have prevented an outbreak, at this point in time," he said.