The island's chief medical officer has barred any passengers or crew from leaving the boat while in port, after a case of measles was diagnosed on the vessel.
Rev. John Carmichael, president of the Church of Scientology in NY, told BeliefNet.com in 2006 that the church does not have any "precepts or strictures" regarding vaccinations as a religious principle.
The church's media centre was not immediately available for comment.
The ship's doctor requested 100 doses of anti-measles vaccines, which have been supplied by the island's Department of Health and Wellness.
"Persons who have taken note of the news would be aware of the current situation in the United States, where there are outbreaks of measles", James said.
Measles is highly infectious for those who aren't vaccinated and confined areas with large gatherings of people, such as a cruise ship, can increase risks of exposure.
A cruise ship in St. Lucia has been quarantined.
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On Thursday, St. Lucia's health agency said it has been discussing the measles case with regional organizations, including the Caribbean Public Health Agency.
"The ship's doctor has the confirmed case in isolation on the ship", Dr Fredericks-James was quoted as saying by NBC. According to officials, the ship is scheduled to leave port before midnight on May 3.
The vessel's home port is Curaçao, a Dutch Caribbean island, but it sails under a Panamanian flag, according to MarineVessels.com.
But two former Scientologists later came forward to say they were held against their will in the depths of the ship and were forced to do hard labour as Cruise and company celebrated above.
In her YouTube announcement, James referred to the current measles outbreaks in the US, and advised residents traveling to the USA 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 almost 300% in the first three months of 2019 compared to the same time frame in 2018, according to the World Health Organization.
Last week, the Centers for Disease Control and Prevention (CDC) recorded the highest number of measles cases in the last 25 years.