Any more passengers who test positive will immediately be taken into specialist NHS care, the department said.
The first case in Israel was announced on Friday.
On Sunday, Kato said he took the latest case "seriously and will strengthen follow-up of passengers", with daily phone calls from local health officials and by asking them to not make any unnecessary outings or use public transport.
The United States, Canada, Australia, and other countries evacuated their citizens from the ship before the end of a two-week quarantine period and are now imposing new quarantine or travel restrictions on those passengers.
The family of David and Sally Abel, from Northamptonshire, said they have now been moved to a "prison-like" hospital.
A total of 138 Indians, including 132 crew and 6 passengers, were among the 3,711 people, on board the ship when it docked at the port.
The patient, who tested negative for the virus during the quarantine February 14 on board the Diamond Princess, returned to her home in Tochigi prefecture, near Tokyo, on February 19, according to national broadcaster NHK.
Japan has been criticised in the face of mounting evidence that the quarantine imposed on the Diamond Princess did little to stop the virus spreading. There has been a total of four deaths so far in Japan, while more than 130 people have been infected excluding the cases on Diamond Princess.
28 total cases of coronavirus found in India: Health Minister
The techie had worked with people from Hong Kong in Dubai last month, where he is suspected to have contracted the disease. Mr Modi has said he will not participate in public celebrations for the Hindu festival of Holi on Monday.
Chief Cabinet Secretary Yoshihide Suga said that over 1,000 passengers and crew will remain on board the ship after the disembarkations.
In Japan, more than 100 people have now tested positive for the flu-like illness, which has killed more than 2,300 in mainland China, where it emerged in the central Chinese city of Wuhan late a year ago. The tourists were diagnosed upon returning home.
The latest fatality is a Japanese man in his 80s who was among the first group of people developing symptoms when Japanese health authorities ordered a 14-day quarantine of the ship on February 5, Masami Sakoi, a health ministry official, said at a televised news conference.
Some 200 Israeli students and teachers were instructed to enter isolation due to being in several tourist sites at the same time as the group.
A team of officials from the World Health Organisation (WHO) visited Wuhan in Hubei province last week to conduct a detailed probe.
The third chartered flight arranged by the Hong Kong Special Administrative Region government arrived in Hong Kong on Sunday morning, bringing back five more residents from the COVID-19-inflicted Diamond Princess cruise ship in Japan.
Hours before the latest United Kingdom cases were confirmed, 118 people were released from a coronavirus quarantine centre in Milton Keynes.
Interior Minister Aryeh Deri was set to sign an order to that effect later in the day.