© Provided by Kent Frasure

TOKYO—Rebecca and Kent Frasure were sitting down to breakfast Friday morning when a stream of ambulances pulled up beside the cruise ship docked at the Yokohama port where they were quarantined for two weeks because of the novel coronavirus.

“Oh, there must be more people,” Mr. Frasure remembers telling his wife. The couple from Forest Grove, Ore., had watched twice previously that week from the balcony of their room on the Diamond Princess as ambulances spirited away people who had tested positive for the virus.

What they didn’t realize: This time the Japanese health authorities were coming for Rebecca.

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“I was just flabbergasted. You’re dumbfounded to be hearing it is you,” said Mrs. Frasure, 35 years old, in a video interview from her hospital bed in Tokyo this weekend.

So far, 70 people aboard the Diamond Princess have tested positive for the virus, according to an announcement to passengers Sunday. They are being treated at hospitals on shore.

Officials have said the outbreak may have begun with a Hong Kong man who disembarked partway through the cruise. Those still aboard have to stay there until at least Feb. 19 as Japan tries to prevent the outbreak, which originated in China and has killed more than 800 people, from spreading to its shores.

What started for the Frasures as a pleasant cruise around Asia, with stops in Vietnam and Hong Kong Disneyland, has now landed Mrs. Frasure in the isolation ward of the infectious diseases unit, while her husband is stuck in his cabin.

The good news is Mrs. Frasure hasn’t had any of the symptoms of the virus, such as fever or coughing. Her temperature was measured at 97.9 degrees Fahrenheit on Sunday, and she said doctors were doing tests but not specifically treating any ailment.

Some 3,700 passengers and crew were on the Diamond Princess as it traveled through East Asia for two weeks. After it arrived in Yokohama at the beginning of February, the Frasures were planning to enjoy a few weeks touring Japan. Instead, the ship’s passengers were placed under quarantine on Feb. 3.

Soon after, Japanese health officials appeared at the door of the Frasures’s 500-square-foot cabin and signaled with gestures that they were going to insert a thermometer in their ears. The couple filled out a questionnaire and said they didn’t have symptoms of the novel coronavirus.

Something about the visit prompted the officials to come back the next day. Mrs. Frasure wonders if it was because they checked boxes saying they had taken painkillers—although that was for regular aches and pains, not a fever. The couple were brought to a room on board the ship where a Japanese doctor and nurse inserted a swab stick in their throats to collect samples.

Then came the knock on Friday during breakfast. This time a crew member was translating for Japanese officials, explaining that Mrs. Frasure had to go but Mr. Frasure, 42, couldn’t join his wife because he tested negative.

“It was pretty surreal to be there at the door and having them tell me, ‘You tested positive. He has to stay on the ship,’” Mrs. Frasure said. She was given an hour to pack her bags, then waited nearly six hours before officials arrived to take her away. Mr. Frasure said he gave his wife a hug.

Mrs. Frasure walked into a waiting ambulance and found another female passenger who would accompany her on the 90-minute journey with flashing lights and no sirens.

At the hospital, she went through a negative-pressure room—an isolation technique to prevent the escape of contaminated air—and was shown to a private room. She went through further tests including a chest X-ray and blood work, and doctors have been checking in.

“I feel fine really still,” she said.

But it is no fun being in a hospital alone where limited English is spoken and nurses carry pocket-size electronic translators. “The pillow is seriously like a napkin. It’s filled with beanbag stuff,” she said, describing a type of pillow preferred by many people in Japan. Meals consist of dishes like tofu and rice.

Mrs. Frasure was told at the hospital that both Japanese and U.S. quarantine laws require her to spend at least another 14 days in isolation. “My concern is not knowing when I will be out of here,” she said. She also said she wondered whether there would be any hurdles going back to her job in customer service at an insurance company.

Meanwhile, Mr. Frasure, who works for a semiconductor company, is sitting through his own quarantine. The staff continue bringing meals for two people. “On the one hand I have extra food,” he said. “Then I sit down and look over, and she’s not there.”

Write to Suryatapa Bhattacharya at Suryatapa.Bhattacharya@wsj.com