Health officials said only those who already have been vaccinated or have previously had measles will be free to leave the 440-foot (134-meter) ship Freewinds, which belongs to the Church of Scientology.
Curacao epidemiologist Dr. Izzy Gerstenbluth told The Associated Press that a small team is assessing more than 300 people aboard the ship, and that the process might take more than a day.
"We will go on board and do our job," he said, adding that authorities have an international obligation to avoid spreading the disease. "If we allow that to happen, measles spreads in places where the risk of severe complications is much bigger, especially when we're talking about poor countries where people have a lower level of resistance."
The Freewinds was under quarantine in St. Lucia earlier this week before it returned to its home port of Curacao early Saturday.
Gerstenbluth said it would be easy to spread the disease given that it's a small ship.
"This is what happens when we don't vaccinate," he said.
Symptoms include runny nose, fever and a red-spotted rash. Most people recover, but measles can lead to pneumonia, brain swelling and even death in some cases.
Measles has sickened more than 700 people in 22 U.S. states this year, with federal officials saying the resurgence is driven by misinformation about vaccines.
Church officials have not returned calls for comment. According to the church's website, the ship is the home of "a religious retreat ministering the most advanced level of spiritual counseling." It says religious conventions and seminars also are held aboard.