Meanwhile, 18 repatriated Americans and one Israeli who returned home from the ship have tested positive, authorities from the two countries announced Friday. Two former passengers have died.
Almost 1,000 passengers were allowed to leave the ship this week after testing negative, but there are now serious concerns about their status.
Earlier this week, officials said six Irish people were travelling on the ship - two of whom had tested positive for COVID-19.
She developed a fever on February 21 and was tested positive on February 22, according to the statement. Her test results came back negative on Feb 15, four days prior to her disembarkation. "We'll find out and take measures", a ministry official told reporters.
As dozens of evacuees from a coronavirus-hit cruise ship begin their two-week quarantine in the United Kingdom, more than 100 others rescued from China are due to be released from isolation.
Because of the need to run the ship and serve the passengers during the original quarantine, crew members could not be properly isolated.
Japan now has three deaths linked to the COVID-19 illness.
Kato has defended Japan's on-board quarantine, telling a TV programme Saturday there was no medical facility large enough to admit more than 3,000 people at once. A total of 36 people who were passengers on the ship are seriously ill on the "infection factory" ship.
The number of cases in Japan grew to 770 as of midday on Sunday, including the cruise ship, after a man in his 70s tested positive in the northern prefecture of Hokkaido, national broadcaster NHK reported.
Some municipalities and companies have also started disclosing information about where infected people work.
Prime Minister Shinzo Abe, speaking at Sunday's government task force meeting, raised concerns about some cases of infection that were of unclear transmission routes.
Thousands of passengers who tested negative for the virus have been evacuated after spending more than two weeks in quarantine on board the Diamond Princess.
Professor Keith Neal, emeritus professor of epidemiology of infectious diseases at the University of Nottingham, said: "The UK authorities brought the passengers home as they would have continued to be at risk staying on the ship".
The cruise ship, owned by Carnival Corp, and carrying some 3,700 passengers and crew, has been quarantined in Yokohama since February 3. It was quarantined after a passenger who disembarked in Tokyo last month was found to be the carrier of the infection. They will also be provided with food, medicine, masks, and other supplies.