Tien Phuoc Nguyen, a 26-year-old Canadian citizen who was cruising with his family, was last seen by other cruise ship passengers jumping overboard Saturday evening as the Adventure of the Seas was passing Mona Island near Puerto Rico and the Dominican Republic.
In a statement released by Royal Carribean spokeswoman Cynthia Martinez, the captain was alerted that a passenger had jumped off the ship, immediately turned the ship around and notified local authorities.
Martinez also stated that onboard security cameras have footage of Nguyen going overboard.
The Coast Guard dispatched a helicopter and rescue boats but there was no sign of Nguyen.
"We will continue to search until we determine that all probability of survival has been extended," Coast Guard spokesman Ricardo Castrodad said.
The Coast Guard believes there is a chance that Nguyen could turn up alive but acknowledged that currents in the Mona Passage area are dangerous.
"Weather conditions there typically change rapidly. It could be a good weather day and a weather system comes in and everything turns and becomes pretty nasty," Castrodad said.
"You can have easily from two to four feet seas and then be facing 10-foot seas from one moment to another, so it is known as a pretty dangerous body of water," he said.
The FBI is also investigating the incident.
The Adventure of the Seas was returning to San Juan after a seven-night Caribbean.