"When the ship is docked, you have to go via the gangway to get off the ship and there's a big security guard there, which will stop you from getting off if you're not allowed to get off", she said. Church officials have not returned messages for comment.
The global 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.
No one has been allowed to leave the ship yet, according to Dr. Merlene Fredericks-James, who told CBS News that the ship remains in port.
The 440-foot Freewinds ship is reportedly owned by the Church of Scientology.
Freewinds, a United States based cruise ship, owned and operated by the Church of Scientology, was earlier this week quarantined in St. Lucia when it was discovered that a passenger had contracted measles. She said the ship's doctor has called for more than 100 vials of measles vaccine.
The boat is docked in the Caribbean island of Curacao and functions as a retreat that is religious, the church website says.
A team of health officers in Curacao plans to board the vessel to determine who aboard may have been exposed to a crew member diagnosed with measles and who aboard has previously been vaccinated against the highly contagious disease, the official said.
"We are aware of the situation in St Lucia and we have been monitoring it. Rest assured that the Ministry of Health will take any measure to protect the public against the introduction of any threatening disease in Antigua and Barbuda", she said.
Public health officials blame declining vaccination rates in some communities driven by misinformation about inoculation that has left those populations vulnerable to rapid spread of infection among those with no immunity to the virus.
Measles is highly contagious and can be transmitted via the air through sneezing or coughing, or by physical contact with an infected person or with an object that the person has touched.
There were about 300 people aboard the ship, according to Saint Lucia authorities, which placed the vessel in quarantine. Symptoms may include fever, cough, runny nose, watery eyes and a rash of red spots.