When Lydia Todman booked a trip to St. Croix with her husband earlier this month, she was hoping only for a relaxing getaway. But when she arrived, she learned she could also get the Covid-19 vaccine.

Ms. Todman, 43, said that local residents she knew on the island encouraged her to book a vaccine appointment. At the time, she and her husband, who is 54 and has asthma, were not eligible for a shot in their home state, Georgia. But in St. Croix, every adult is eligible. So she visited the territory’s Department of Health website, saw they had appointments available for the next day, and signed up.

“We were in and out within a matter of a few minutes,” Ms. Todman said. “It was amazing.”

Nearly 106,000 people call the U.S. Virgin Islands home, and the territory has administered more than 33,000 Covid-19 vaccines to date, with about 10,600 people now fully protected with two doses. At a news briefing on Monday, the governor, Albert Bryan Jr., estimated that at most 3 percent, or approximately 1,000 of those vaccines, have gone to tourists.

“Have we become aware of the fact that people are seeking us out? Yes. And you know, we accommodate everyone,” said Angela East, the coordinator and director of the Covid-19 vaccine program at Plessen Healthcare, which has administered 44 percent of all Covid-19 vaccines in the territory. “We are going to give you the shot in the spirit of putting as many shots in arms as possible.”

Health authorities and ethicists don’t see a big problem with the vaccine tourism in the U.S. Virgin Islands, given the ample supply of the shots and high levels of vaccine hesitancy among residents there. And the trend may wane as more U.S. states open up their eligibility criteria. Still, wealthy Americans traveling to the Caribbean to secure Covid-19 vaccines is an example of the many ways in which vaccine access across the world is shaped by race, circumstance and privilege.

In St. Croix, St. John and St. Thomas, the three largest of the U.S. Virgin Islands, vaccines are readily available to tourists partly because of vaccine hesitancy, “which is very high in the Virgin Islands,” said Dr. Tai Hunte-Ceasar, the medical director of the territory’s Department of Health. This hesitancy seems most pronounced among residents of color, Mr. Bryan said at the news briefing. “Caucasians that live in the Virgin Islands are more apt to take the vaccine and take it quicker,” he said.

When Bridget Platten, 40, who works in sales in New York City, received her Covid-19 vaccine in St. Croix, she was encouraged to tell friends to get inoculated, too. “The doctor said: ‘Listen, I have all this vaccine. And people are afraid to get it here,’” Ms. Platten recalled. “‘If you have any friends, or there’s anyone you know who wants a vaccine, please have them call me.’”

Some Americans have flown to the island specifically to be vaccinated. “My friends from New Jersey went, and the most probing question they faced was, ‘Will that be Pfizer or Moderna for you?’” said Rob DeRocker, a marketing consultant from Tarrytown, N.Y., who spends winters in St. Croix. “The result has been a mini boom of visitors on an island whose tourism economy, like most others, has been brutalized by the pandemic.”

This boom has been aided by the fact that since March 1, everyone over 16 has been eligible to get the vaccine in the Virgin Islands — so tourists don’t even have to worry about cutting in line. The territory accommodates about 100 walk-ins each day, too. “Nowhere else in the U.S. can you actually just walk in and get the vaccine, anybody over 16,” Mr. Bryan said on Monday. On March 1, the islands also opened two federally supported community vaccination centers on St. Thomas and St. Croix.

U.S. travelers also face less red tape when visiting the U.S. Virgin Islands compared with other Caribbean destinations. If they submit a negative coronavirus test within five days of leaving for the territory, or a positive antibody test taken within four months, they do not have to quarantine upon arrival. Travelers to Jamaica and Barbados, in contrast, are asked to quarantine no matter what. And U.S. travelers can’t visit the Cayman Islands unless they conform to strict eligibility criteria.

Dr. Hunte-Ceasar said that, at this point, the Department of Health did not consider vaccine tourism to be a problem. “We definitely want to ensure the local residents get vaccinated,” she said. But “we have not had any shortages by serving both populations.” The Virgin Islands currently have 27,000 doses of the Pfizer vaccine, 18,900 doses of the Moderna vaccine, and 600 doses of the Johnson & Johnson vaccine available, said Monife Stout, the department’s immunization director.

Noreen Michael, a scientist at the University of the Virgin Islands who studies health disparities, agreed that it was crucial to ensure that vaccines are available to residents who want them, but said she had not seen evidence to suggest that tourists are taking vaccines away from residents who want them. “On the public health side, it’s a plus,” she said. “On the equity side, I don’t see it as significant issue.”

Perhaps, too, vaccine tourism could be used as a force for good — to secure doses for marginalized groups in other regions. Although the Virgin Islands provide free Covid-19 vaccines, the islands could charge tourists for their vaccines, and the funds could be used to send vaccines to regions that need them, said Felicia Knaul, an international health economist at the University of Miami. “Could we send those vaccines to Jamaica, or to the Dominican Republic or Haiti?” she asked. “Once you’ve gotten past the key welfare and human rights aspects, if you can use that funding to pay for people who right now have no access, I think it’s worth thinking about.”

For now, health authorities are focused on ways to reduce vaccine hesitancy in the territory. “People access misinformation and perpetuate lies and things that are harmful,” Dr. Hunte-Ceasar said in a news conference last week. As a result, the islands have been experiencing a surge in cases and hospitalizations that she said give her “chest pain and heartburn every night.” Although vaccine hesitancy does seem to be decreasing, residents will need to start widely embracing the vaccine if the islands are to meet their goal of vaccinating 50,000 Virgin Islanders by July 1.

In the meantime, visitors from the continental U.S. will continue to take advantage of the extra doses. Some have stayed longer than they planned, too — and have even contemplated moving to the islands for good.

“I started falling in love with the culture of St. Croix,” said Hemal Trivedi, a documentary filmmaker who lives in Weehawken, N.J., and was vaccinated in St. Croix in February. “Toward the end of the trip, we were actually looking for a place to buy.”