The ship, sitting upright in waters off the Italian island of Giglio, is supported by large pontoons welded to its sides. They are designed to help the ship float before it's towed away later this year.
Officials said there were no injuries, and work to prepare the ship for its removal, and eventual scrapping, will proceed Wednesday.
The ship has been in place since it ran aground and keeled over in January 2012 with 4,229 people aboard, killing 32 people on board.
The removal project is the biggest salvage operation of a passenger ship ever undertaken.