Twenty-year-old Bianca D'Silva is being treated in a Japanese hospital, where her parents and 14-year-old brother are also in isolation pending test results, the Herald Sun reports.
"It was a bit of a shock," the law student told the newspaper of her diagnosis, which came after she developed a fever and headaches.
"You never think this is going to happen to you.
"It's a bit of a struggle but what can I do. Physically I am fine – it was just like I have the cold.
"Now I just have to wait for it to clear."
Nine News reports the woman will be forced to spend her 21st birthday in a Japanese hospital after contracting the illness.
The Diamond Princess is docked in the port of Yokohama with more than 3700 passengers, including more than 200 Australians, stranded for a week.
Ms D'Silva's grandfather Peter Vieyra told the newspaper it was a "very bad" situation, and that the family had been stuck in small cabins.
"We are feeling very devastated and terribly sad also," he said.
"They are all traumatised and mentally and physically exhausted."
Authorities are yet to confirm Ms D'Silva's case, while Princess Cruises said 11 Australians on board 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.
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