Footage showed panicked passengers hanging on to the sinking catamaran on Sunday morning before they were saved.
The 15-metre catamaran, named Serenity, had suffered a hatch failure, causing theship to fill with water in the North Atlantic Ocean.
The passengers launched a distress call to the US Coast Guard, which issued an emergency alert that was picked up by Disney Treasure at 11.40am.
The 339-metre-long Mickey Mouse-themed liner, which was on its maiden voyage 120km away, launched a small boat that rescued all four passengers, none of whom suffered injuries, an hour later.
A spokesman for the cruise line said the Disney Treasure had been heading from Eemshaven in the Netherlands to its base in Port Canaveral, Florida, when it received the call.
Catamarans are made up of two parallel hulls, connected by a single deck. They can look anything like a lightweight boat to huge passenger ferries.
Disney Treasure is yet to be used by the general public and is the sixth of its kind owned by Disney Cruise Line fleet.
It will launch its maiden voyage for passengers from its Florida base on December 21 and will offer seven-night cruises in the eastern and western Caribbean.
It has more than 1250 staterooms, 10 pools, Disney-themed restaurants and immersive spaces also inspired by Marvel, Star Wars and Pixar.