By Miguel Bustillo and Laura Stevens 

DALLAS--A Texas health-care worker who may have had contact with clinical specimens from the first man diagnosed with Ebola in the U.S. has self-quarantined onboard a Caribbean cruise ship, the U.S. Department of State said Friday.

The unnamed health-care worker from Texas Health Presbyterian Hospital Dallas left the U.S. via a Carnival Cruise Lines ship on Oct. 12 from Galveston, Texas.

"We are working with the cruise line to safely bring them back to the United States out of an abundance of caution," the State Department said.

Carnival said the passenger, a lab supervisor at the Dallas hospital, hasn't exhibited any symptoms of the virus and isn't considered a risk to any other passengers or crew.

The cruise ship's doctor has monitored the worker and she is said to be in good health, but she is voluntarily isolated in a cabin along with her travel companion as a precaution, the State Department said.

The ship, the Carnival Magic, has a guest capacity of 3,690 and onboard crew of up to 1,367, according to the company website. It is based in Galveston and operates seven-day cruises to the Caribbean, the company said in a statement. The ship is scheduled to return to Galveston on Sunday.

The hospital worker was considered at very low risk for contracting Ebola and was originally only required to self monitor for possible signs of the disease. The person "was out of the country before being notified of [the Centers for Disease Control's] updated requirements for active monitoring," the State Department said.

Texas and federal authorities tightened monitoring requirements this week after two nurses who treated the initial Ebola patient, Thomas Eric Duncan, contracted Ebola. It was at that point, after more active monitoring began, that "it was discovered that an employee...had departed the United States," the State Department said.

The hospital said it had no immediate information on the matter.

The worker has been checking her temperature daily since Oct. 6, and hasn't had a fever or any other signs of illness. It has been 19 days since the person was potentially around Mr. Duncan's fluid samples, near the end of the 21-day period when a person is believed to be likely to contract the disease.

The government of Belize said in a statement Thursday night that it had been contacted by the U.S. about transporting the woman through the country's Philip S.W. Goldson International Airport, but said that "out of an abundance of caution" declined to facilitate the request.

"The passenger never set foot in Belize," the Belize government statement said.

Write to Miguel Bustillo at miguel.bustillo@wsj.com and Laura Stevens at laura.stevens@wsj.com

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