The United States Coast Guard said it was searching for missing crew member Arron Hough, 20, who fell off the ship 267 miles northwest of Aguadilla in Puerto Rico.
Talent agency Russell Smith Associates said in July that Mr Hough would be joining the cast of Grease The Musical on the vessel.
The agency said he was a new graduate of the Urdang Academy, a dance and musical theatre college in London.
The college tweeted that they were praying for Mr Hough and his family on Wednesday night.
Royal Caribbean said a member of its entertainment team on the Harmony of the Seas ship did not report to work as scheduled on Tuesday 25 December.
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 says its care team is providing support to the family, adding that its “thoughts and prayers are with them during this difficult time”.
Harmony of the Seas is currently sailing on a seven-night itinerary that left Fort Lauderdale, Florida, on Sunday.
Its scheduled stops are Philipsburg in St Maarten, San Juan in Puerto Rico and Labadee in Haiti.
The Foreign Office said: “We are providing assistance to the family of a British man who has been reported missing off Fort Lauderdale.”
The US Coastguard said in a statement: “The Coast Guard is searching Wednesday for a missing crew member, who went overboard from the Royal Caribbean cruise ship Harmony of the Seas 267 miles northwest of Aguadilla, Puerto Rico.
“Missing is Arron Hough, 20, of the United Kingdom.
“Watchstanders at Coast Guard Sector San Juan received a notification from the cruise ship stating a crew member went overboard Tuesday.”
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A HC-130 Hercules airplane crew from Clearwater and the crew of the Coast Guard Cutter Resolute are searching for him.
The Royal Caribbean website says the Harmony of the Seas is the first ship to feature the Broadway hit musical Grease as part of its entertainment programme.