St Lucia's chief medical officer Dr. Merlene Fredericks-James told the media that the case was being taken very seriously.
"It is therefore likely that other persons on the boat may have been exposed". It's scheduled to leave at 11:59 p.m. on Thursday night.
The vessel in question, named "Freewinds", is now moored outside the St. Lucia coast.
The church's media centre was not immediately available for comment.
Officials have declined to name the ship involved, the report says.
According to CNN, health officials received a tip from two sources that someone on board the Freewinds had measles, a highly contagious virus that is easily spread by coughing, sneezing, and really any contact with the infected person.
Fredericks-James said health officials were using authority given to them by the nation's quarantine act and public health act. St. Lucia learned about the crew member's condition from a International Health Regulation focal point official in the Dutch Caribbean and then verified the diagnosis through other health agencies, the St. Lucia health department said.
Our epidemiological investigation aboard the ship has verified that the confirmed case, as well as other crew and passengers are stable, and remain under surveillance by the ship's doctor.
However, the Hollywood Reporter has written that "a notable number of the highest-profile immunization dissenters are Scientologists" who have helped "inflame the vaccine wars". It says the vessel's home port is Curacao. The restriction comes as the number of measles cases in the United States has reached a 25-year peak with more than 700 people diagnosed as of this week, part of an worldwide resurgence in the disease.
Fredericks-James ended her statement with a warning to the people of St. Lucia to make sure they and their children are up to date with their vaccinations, especially since many travel to and from the United States, where "there is a situation going on".
The vast majority of US cases have occurred in children who have not received vaccines against measles, mumps and rubella (MMR), officials said.