Frank Wucinski and his 3-year-old daughter, Annabel, are among the dozens of Americans the government has flown back to the country from Wuhan, China, and put under quarantine to check for signs of coronavirus.

Now they are among what could become a growing number of families hit with surprise medical bills related to government-mandated actions.

Mr. Wucinski, a Pennsylvania native who has lived in China for years, accepted the U.S. government’s offer to evacuate from Wuhan with Annabel in early February as the new coronavirus spread. His wife, who is not an American citizen and remains in China, developed pneumonia that doctors think resulted from Covid-19, the disease caused by the respiratory virus. Her father, whom she helped care for, was infected and recently died.

The first stop for Mr. Wucinski and Annabel was a two-week quarantine at Marine Corps Station Miramar near San Diego. During that time, they had two mandatory stays in an isolation unit at a nearby children’s hospital. The first started upon arrival in the United States, and the second was a few days later, after an official heard Annabel coughing.