The girl’s family have not yet been quizzed by detectives but police have said they believe the incident was a tragic accident.
Elmer Román, of the local Department of Public Security, said: “Police have now launched an investigation and are trawling CCTV of the ship.
“At this time (the Division of) Homicide is in place. It has not been possible to interview the family.
“It is a very strong scene, very sad and tragic.
“At one point, one of her grandparents… in an act of games, exposes the girl to the void and falls out of his hands.”
The boat has a height of around 210 feet and the 11th floor will have been around 150 feet above land level when the vessel was docked.
It holds around 4,000 passengers and was ending a seven-day Southern Caribbean cruise of Antigua, St Lucia and Barbados at the time of the tragedy.
Royal Caribbean has been contacted for comment.