Fredericks-James said St. Lucia authorities were not holding the boat.
The vessel had arrived in St Lucia from Curacao on Tuesday, when it was placed under quarantine by health authorities because of a measles patient - a female crew member, according to Merlene Fredericks-James, St Lucia's chief medical officer.
Others would likely be restricted from leaving the vessel for the duration of the incubation period - the time during which they could potentially transmit the disease to others, he told Reuters by telephone.
"An investigation will also be done to determine who will be allowed to leave the ship without (posing) a threat to the population of Curacao", it said. "There is no other way than ... by not allowing anyone who may be infected off the ship".
The disease is extremely contagious.
Gerstenbluth said the infected crew member had travelled to Europe and rejoined the ship on April 17, then reported feeling ill on April 22.
The worldwide vessel-monitoring website MarineTraffic.com also showed that a Panamanian-flagged passenger ship identified as SMV Freewinds docked in port near the St. Lucia capital of Castries.
Everyone on board the ship is forbidden from disembarking by authority of St. Lucia's health officials under their quarantine act and public health act.
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The Freewinds ship is reportedly owned by the Church of Scientology.
On its website, the Church of Scientology explains that for a Scientologist, boarding the Freewinds is "the pinnacle of a deeply spiritual journey".
It says the boat is based in Curacao, an island once part of the Dutch Antilles north of Venezuela and now an autonomous country within the Kingdom of the Netherlands.
The Church of Scientology didn't respond to CNN's request for comment.
"Quarantine is a word that people respond to very strongly, but it's actually one of the strongest tools in the public health tool kit", Katz said.
Measles has sickened more than 700 people in 22 US countries this year, with national officials stating that the resurgence has been driven by misinformation regarding vaccines.
In April, the World Health Organisation warned that measles cases rose exponentially in 2019, with the number of cases rising by 300 per cent within the first three months of this year.