The passenger, from Sydenham in the city's outer northwest, would be the 12th Australian to be diagnosed on the ship, which is currently docked in the port of Yokohama.

Her grandfather, Peter, who did not give his last name, said she was taken off the ship with her parents and younger brother and transported to a hospital about two hours from the port.

"My granddaughter Bianca, who is 21 years old, tested positive and now she's in isolation in the hospital and my three other family members are all in isolation wards over there," he told 3AW radio on Wednesday.

More than 3700 passengers, including about 200 Australians, have been stranded on the ship for a week after dozens of people tested positive for the coronavirus.

Peter said the Australians aboard haven't heard from the government since they were quarantined.

"These people are in limbo and no one cares about them," he said.

"That's how it seems because we've had no contact from the government in any way."

Peter said the family had been struggling both mentally and physically, as a result of being trapped in their cabins prior to the diagnosis.

"They were locked up in these two little rooms, 3x3 perhaps, without any access to clean air or anything," he said.

Authorities are yet to confirm the case, while Princess Cruises said 11 Australians aboard were affected.

"We are following guidance from the Japan Ministry of Health on plans for disembarkation protocols to provide medical care for these new cases," it said.

"Since it is early in the quarantine period of 14 days, it was not unexpected that additional cases would be reported involving individuals who were exposed prior to the start of the quarantine."

The quarantine end date remains February 19 unless there are any unforeseen developments.

Princess Cruises has confirmed all guests aboard the cruise will be refunded their fare, including air travel, hotel, ground transportation and other expenses.

Australian Associated Press