The person is not showing symptoms of the disease and is voluntarily remaining in their cabin, it said.
"It has been 19 days since the passenger may have processed the since deceased patient's fluid samples," the department said in a statement.
But the State Department is working with the cruise line "to safely bring them back to the United States out of an abundance of caution," it said.
"The employee did not have direct contact with the since deceased Ebola patient, but may have had contact with clinical specimens collected from him," it said.
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This was a reference to Liberian sufferer Thomas Eric Duncan, who died in a Dallas hospital October 8.
The person left the United States on the cruise ship before the Centers for Disease Control and Prevention updated its requirements for monitoring of people who may have had contact with Duncan, the statement said.