Dr. Merlene Fredericks James said in a YouTube video on Tuesday that the cruise ship was being quarantined because of fears that others on the ship may be infected.
James did not name the cruise line or the boat, and did not say where it came from.
"Measles, we know, is a highly infectious disease...So because of the risk of potential infection, not just from the confirmed measles case but from other persons who may be on the boat at the time, we thought it prudent to make a decision not to allow anyone to disembark," she said. "The Ministry of Health continues to work with all authorities."
In her YouTube announcement, James referred to the current measles outbreaks in the U.S., and advised residents traveling to the U.S. and other parts of the world that they ensure they and their children are adequately vaccinated against the disease.
Preliminary global data showed that reported cases of measles have been up nearly 300% in the first three months of 2019 compared to the same time frame in 2018, according to the World Health Organization.
ABC News' Meghan Keneally contributed to the reporting in this story.