Marco Fidel Castro picked up his severed thumb and went immediately to see the ship's doctor, attorney Jordan Wagner told the Orlando Sentinel.
He was treated by a nurse who bandaged the wound and the thumb was put on ice.
When the ship eventually docked in Puerto Rico two days later, Castro was told by a doctor it was too late to reattach the thumb, Wagner said.
Castro's lawsuit is seeking undisclosed damages for Disney's failure to provide timely and adequate medical care and failure to ensure the safe operation of cabin doors.
"He was near the hallway door with his thumb on the door frame and his wife was holding the door open with her foot. She moved and her foot came away and he didn't realize the door was closing. The door slammed shut with force," said Wagner.
Disney Cruise Line has not responded publicly on the lawsuit, the Sentinel reports.