The ship's doctor requested 100 doses of anti-measles vaccines, which have been supplied by the island's Department of Health and Wellness.
The USA is currently in the midst of the largest measles outbreak in 25 years, in spite of having previously eradicated the disease.
While St Lucia's department of health did not identify the ship, it was named by St Lucia Coastguard as the "Freewinds" in an interview with CNN.
The Port Authorities schedule confirms that the vessel arrived in Port Castries on the Tuesday and is scheduled for a Thursday departure.
The Freewinds is a 140-metre ship, owned and operated by the Church of Scientology.
The Church's website describes Freewinds as "a religious retreat ministering the most advanced level of spiritual counselling in the Scientology religion."
300 people are thought to be onboard the affected vessel.
In a statement to the Hollywood Reporter the Church of Scientology regarding vaccination said "it takes no position one way or the other on this issue."
John Carmichael, president of the Church of Scientology in New York explained to the Beliefnet website that there was not official stance on vaccinations "as a religious principle."
"Scientologists are pretty independent people, though I will say this: they tend to do a little more research, perhaps, on the effect of various medical procedures or whatever," he said. "They make their own decisions, but those aren't decisions that the church tries to influence in any way."
Fredericks-James said the department of health would "continue to support them as needed," and that "the ship is free to leave our ports at any time".
St Lucia declared itself free of measles in 1990.