Her infection with the coronavirus confirmed after her death, Kato said. Prefectural officials said he is in serious condition.
The woman fell ill in January but only later showed symptoms of pneumonia and was hospitalized, then transferred to another hospital when her condition worsened.
He first developed a slight fever on Jan 31, but returned to work from Feb 3 to 5 after taking medicine to bring down his fever. Another doctor working at the hospital, along with two patients who saw doctors there, are reportedly suspected of having contracted the virus. The ship now has 218 people infected with the virus out of 713 tested since it entered Yokohama Port on February 3, the largest cluster of infections outside China.
None of the five cases - the surgeon, his patient, the elderly woman, the taxi driver, and the employee - had any record of recent overseas travel at all, let alone to Wuhan, ground zero of the coronavirus outbreak. He is the first medical doctor to be infected in Japan. She was the first fatality in Japan, and the third outside mainland China.
The fever rose to 38 C on Saturday, and a CT scan revealed symptoms of pneumonia.More news: Netflix defends itself against new transmission rivals through the Samsung association
A health ministry official could not confirm how many of those infected so far on the ship were crew.
Both Suga and health minister Katsunobu Kato said there was no evidence the coronavirus, dubbed SARS-CoV-2, was spreading widely in Japan, although Kato said that it might and that the government needed to prepare for that situation.
He said the number of people confirmed to have the virus in Japan had risen to 33, with another 218 on a cruise ship quarantined at a port in Yokohama.
The taxi driver is the son-in-law of the elderly woman who died. "We should assume that the virus has already been spreading in Japan", he said.
Still, their occurrence in the major metropolitan areas of Tokyo and Kansai have raised concerns of a stealth outbreak of Covid-19.More news: The All-Star Game of the worldwide records
The ship was quarantined on arrival in Yokohama, near Tokyo, on February 3 after a man who disembarked in Hong Kong before it traveled to Japan was diagnosed with the virus, which has now killed more than 1,350 people in mainland China.
The government has made a decision to allow passengers older than 80 to get off the ship after testing negative for the virus, Kato said.
"There are some people whose health may deteriorate by staying aboard for an extended period", said Mr Kato earlier on Thursday.
Japan is of the countries worst affected by the epidemic outside China, with 251 confirmed cases, including those on the Diamond Princess.
Later Thursday, Prime Minister Shinzo Abe announced a 15.3 billion yen ($139 million) economic package to fight the virus, including funding for the development of vaccines and virus test kits, support for hundreds of returnees from Wuhan and measures to strengthen border controls to minimize the spread of the virus in the country.More news: Coronavirus: Ninth case diagnosed in United Kingdom as virus spreads to London