The Bahamas-registered Enchantment of the Seas, owned by Royal Caribbean, picked up the 14 in the early morning hours Saturday near the island of Cozumel, on Mexico's eastern Yucatan peninsula.
The Cubans disembarked wearing the ship's crew uniforms and were taken to immigration offices in Cozumel, in the Mexican state of Quintana Roo.
Some of the Cubans received medical care.
Escapees from Cuba's communist system are frequently picked up after hazardous trips across the Caribbean to Mexico, the United States and other countries.