"One person is dead and four are injured, including two whose lives are in danger," a spokesman for the fire service told AFP.
The lifeboat "became detached" from the ship with five people on board, the spokesman said, but there was no immediate confirmation of reports that they had been taking part in a safety drill at the time.
The 120,000-tonne liner operated by Florida-based Royal Caribbean only just entered service in May.
It has 16 decks and can carry more than 6,000 passengers and 2,400 crew.