The ship was 267 miles northwest of Aguadilla, Puerto Rico, at the time. The US Coast Guard has said it is searching for Arron Hough.
A spokesperson for Royal Caribbean confirmed a member of the entertainment team had not reported to work as scheduled on Tuesday, while the ship was en route to Philipsburg, St Maarten, BBC News reports.
"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," the spokesperson said.
"Local authorities were notified and a ship-wide search for the crew member was conducted.
"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."
The US Coast Guard said: "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.”
Hough was understood to have joined the cast of Grease The Musical on the vessel.
His talent agency, Urdang Academy said it was shocked and saddened by the news and that staff were praying for Hough and his family.