The move came a day after neighbouring Belize denied entry to one of the passengers, a Dallas woman who may have come in contact with the virus through laboratory work, Xinhua reported citing local media.
Local port authorities in Quintana Roo, the Caribbean state Cozumel is located in, said Mexico was implementing the necessary international health protocols, following a health alert issued by Belize.
"We woke up to several international notifications, and even though the(Ebola) case is not confirmed, the state health ministry in coordination with the municipality and port captaincy made the decision" to deny docking, Mexico's El Universal news website cited the municipal president of Cozumel, Freddy Marrufo, as saying.
Cruise operator Carnival Cruise Lines said the passenger was in isolation on the ship, though she has shown no symptoms of the disease, and poses no threat to other passengers.
On Wednesday, the cruise company was notified of the potential health risk by the US Centers for Disease Control and Prevention (CDC) who said the woman supervised the laboratory at the Texas Health Presbyterian Hospital, where patient Thomas Duncan had been treated before dying of the disease.