The officer is already in hospital and had self-isolated as a precaution.
The ministry says the quarantine official was on the ship on February 3 and 4. The ship, carrying 3,711 passengers, has an unspecified number of Indians on board.
The disease has killed 908 people, chiefly in mainland China, and infected more than 40,000.More news: Google accidentally posts Android 11 dev preview page, then takes it down
He was not diagnosed with coronavirus until he left the ship on January 25.
A girl on Christmas Island who was previously isolated has tested negative, while in Australia, five of the 15 confirmed cases of coronavirus have been cleared. Four were in serious condition, Kato said.
All those infected with the disease have been brought ashore for treatment, while the other passengers remain confined to their rooms on board until the quarantine period ends, the ministry said.
Passengers have been allowed on decks in shifts to get fresh air and encouraged to regularly take their temperature.More news: Japan confirms first death from coronavirus
Yardley Wong, who is quarantined on board the Diamond Princess, said the latest rise in confirmed cases was making her anxious.
Fellow passenger Yardley Wong tweeted: "Anxiety uprisen" on news of the new cases, saying she didn't know whether she or her family might be next.
Meanwhile, the operator of the ship on Monday vowed to refund all 2,666 passengers due to the on board outbreak of the new coronavirus.
A Department of Foreign Affairs and Trade spokesman said the department is urgently seeking advice from Japanese authorities on the new Australian cases.
"The numbers are rising every few days".More news: Vietnam quarantines commune of 10000 over coronavirus
"We are following guidance from the Japan Ministry of Health on plans for disembarkation protocols to provide medical care for these new cases". At least two report back to us on Facebook that they are symptom-free, ' added the man, who declined to be identified.