Almost 300 of the 3,700 people on the Diamond Princess have been tested so far. The number of infected could rise as testing continues.
The checks began after an 80-year-old Hong Kong man who had been on the ship last month fell ill with the virus.
All 10 cases are in those over the age of 50, Japanese broadcaster NHK said.
Four are in their 50s, four are in their 60s, one is in their 70s, and another one is in their 80s. Two of them are said to be Japanese, and none are in "serious condition", NHK said.
Japanese Health Minister Katsunobu Kato said the confirmed cases were among 31 results from 273 people tested so far.
"We had them [the ones who tested positive] get off the vessel and... we are sending them to medical organisations," he said at a news conference on Wednesday.
How did the virus get on board?
In China alone, there are now more than 24,300 cases of the virus, with the death toll at 490.
There is a much smaller number of cases in other countries around the globe - two people outside of mainland China have died of the disease.
The Hong Kong man believed to be the source boarded the cruise ship in Yokohama, Japan, on 20 January, and disembarked in Hong Kong on 25 January. He was only later found to have tested positive for the virus.
Officials on the cruise ship began screening guests on Monday evening, and the vessel was placed under quarantine on Tuesday.
What happens to the passengers now?
Passengers and crew on the ship will now be under quarantine for 14 days. The incubation period of the virus is believed to be around two weeks.
"We are now officially in quarantine. We are to remain on board the ship and we are confined to our cabins," a British passenger identified as Mr Abel told the Press Association news agency.
Another passenger said her mother, who is in her 80s, was running out of medicine.
"We are in trouble because [her] medicine is running out. Many of the passengers are old and some are as troubled as we are," she told NHK.
The Diamond Princess cruise ship is part of the Princess Cruises line, owned by British-American cruise operator Carnival Corporation.
There are now 20 confirmed coronavirus cases in Japan, excluding the cruise ship infections.
Last week, more than 6,000 people onboard a cruise ship in an Italian port were put on lockdown over fears that a Chinese passenger could be carrying the virus.
The passenger later tested negative for coronavirus. BBC