Arron Hough, who was working on the Harmony of The Seas, went overboard 267 miles northwest of Aguadilla, Puerto Rico, the Coast Guard said in a statement.
Royal Caribbean said Hough failed to show up for work as scheduled on Christmas Day. It added that the ship's closed-circuit camera footage showed him entering an area on Deck 5 around 4 a.m. and he was not seen again. Deck 5 houses shops, restaurants and theaters.
The cruise ship notified Coast Guard Sector San Juan about the missing crew member on Christmas Day, the Coast Guard said.
The cutter Resolute and a HC-130 Hercules airplane from Coast Guard Air Station Clearwater were searching for Hough, it added.
On Twitter, London talent agency Russell Smith Associates, which represents Hough, said: "We are both shocked and saddened about the news concerning our Arron Hough. Our thoughts are with all of his friends and family and we hope for him to be found very soon."
In July, the agency announced Hough was joining the cast of "Grease -- the Musical" on board Harmony of the Seas.
Harmony of the Seas is the world's largest cruise ship. It is currently sailing on a seven-night itinerary that departed Fort Lauderdale, Florida, on December 23, with planned port calls to Philipsburg, St. Maarten; San Juan, Puerto Rico; and Labadee, Haiti.
On December 16, a 22-year-old Georgia man with autism went overboard on a Mexico-bound Carnival Fantasy cruise.
Luke Renner, of the Atlanta suburb of Johns Creek, climbed over a deck rail the day after the ship departed from Mobile, Alabama, according to Carnival Cruise Line. He was traveling with a nonprofit organization that works with disabled adults.
On December 14, a Carnival Victory cruise ship arrived back in Miami after a 26-year-old male passenger went overboard earlier that day, the cruise line said. The man went overboard about 35 miles south of the Florida Keys, officials said.