The woman's diagnosis was confirmed after her death and she had no obvious link to China's Hubei province, the epicentre of the outbreak, Japanese media reported.
What is happening on the Diamond Princess?
The vessel is in quarantine in Yokohama. Not all the 3,700 people on board have been tested yet.
People with the virus are taken to hospitals on land to be treated, while those on board are largely confined to their cabins.
However, on Thursday Japan said it would allow those aged 80 or over who have tested negative for the coronavirus to disembark.
Health Minister Katsunobu Kato said they could be allowed off the ship as early as Friday but would have to stay in accommodation provided by the government, the Japan Times reported.
Meanwhile, another cruise ship - the MS Westerdam - carrying more than 2,000 people docked in Cambodia after being turned away by ports in Japan, Taiwan, Guam, the Philippines and Thailand despite having no sick patients on board.
What's behind the Hubei spike?
Until Wednesday's increases, the number of people with the virus in Hubei was stabilising.
The new cases and deaths in the province have pushed the national death toll above 1,350 with almost 60,000 infections in total.
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