The crewman, Arron Hough, who is 20-years-old, was a performer in the musical "Grease" on Harmony of the Seas, according to Hough's Twitter account.
Royal Caribbean International confirmed that the British member of the entertainment team didn't report to work as scheduled on December 25, according to Sky News outlet.
The company added: "We are saddened to report that after a review of the ship's closed-circuit camera footage, he was observed entering an area on Deck 5 at around 4am and was not seen again."
"Local authorities were notified and a ship-wide search for the crew member was conducted."
The company also said: "Our Care Team is providing support to the family and friends of our colleague, and our thoughts and prayers are with them during this difficult time."
At the moment, "Harmony of the Seas" is continuing on its regularly scheduled 7-night itinerary.