Company spokeswoman Cynthia Martinez said Sunday that the captain of the Adventure of the Seas stopped the ship, turned around and alerted authorities after a passenger reported seeing the person going overboard late Saturday. In a Sunday email, Martinez said footage of the incident was also captured by the ship's cameras.
The missing person's identity, gender and nationality have not immediately been released.
When the U.S. Coast Guard assumed control of the search early Sunday, the cruise ship resumed its trip to Puerto Rico's capital of San Juan.
The Royal Caribbean ship was finishing a seven-night trip and returning to San Juan.