Dr Merlene Fredericks James, chief medical officer on St Lucia, said there was a confirmed case of measles on board and "thought it prudent that we quarantine the ship".
Measles on board the ship
Nobody on board the ship is allowed to leave until further notice.
Dr Fredericks James said on Tuesday (30 April) in a video statement posted on YouTube that "two reputable sources" had confirmed the case of measles on board the ship.
Measles is highly infectious, and for this reason the quarantine has been deemed necessary, the doctor explained.
In the US, cases of measles are at a 25 year high, and Dr Fredericks James also cited this as a reason for the caution.
Nobody allowed to leave the ship
She said, “One infected person can easily infect others through coughing, sneezing, droplets being on various surfaces.
“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."
According to the St Lucia coast guard, the ship is called the Freewinds and is a 440ft (134m) vessel owned and operated by the Church of Scientology.
300 passengers on board
It is believed to have around 300 passengers on board.
The patient with measles on board the boat has apparently been isolated by the ship’s doctor on board, and is in a stable condition.
The ship is within its right to leave the island, and is due so at 23:59 local time on Thursday (03:59GMT).
The Church of Scientology has so far not commented on the case.
The 25 year high in measles cases in the US is attributed to the anti-vaccination movement, which has gained popularity online and falsely claims that the measles vaccine causes autism.
Scientology has never discouraged members from vaccinations.