State Department spokeswoman Jen Psaki said in a statement Friday that the woman had shown no signs of the disease and has been asymptomatic for 19 days.
The government is working to return the woman and her husband to the U.S. before the ship completes its cruise. The White House said the State Department was working to secure their transportation home.
A White House official who was not authorized to be named and requested anonymity said the cruise ship had stopped in Belize but officials there would not allow the passenger to leave the vessel.
Psaki said that when the woman left the U.S. on the cruise ship from Galveston, Texas, on Oct. 12 health officials were requiring only self-monitoring.