TOKYO—The pools, hot tubs and bars of the Diamond Princess emptied out on Feb. 5, when authorities quarantined the luxury cruise ship at a Yokohama dock. Instead of overflowing buffets, staff in surgical masks deliver boxed meals and snacks, about 11,000 a day.

Life has taken a turn for the nearly 3,500 passengers and crew aboard the $500 million vessel who entered a second week under quarantine for the coronavirus disease.

“I...