The Grandeur of the Seas was en route to the Bahamas from Baltimore when the fire broke out on the third deck of the ship.
Passengers and crew members reported to evacuation stations.
The fire was put out about two hours later. There were no reports of injuries.
"People were panicking because we had no idea what was going on," said ship passenger Danielle Miller. "And before we went to bed, there was a pretty bad storm and the ship was really rocking, so our first thought was that we were sinking."
The National Transportation Safety Board and the Coast Guard were investigating the cause of the fire.
The ship sailed from Baltimore on Friday. Some passengers were staying on the ship while it's docked in Freeport, Bahamas. Others were being put up at area hotels.
The remainder of the cruise was canceled. It was not immediately known when the passengers would be able to return home.
In a statement released Monday, Royal Caribbean International said in part:
"Royal Caribbean International will provide each guest with a full refund of the cruise fare paid. ... We will be providing each guest with a future cruise certificate for 100% of the cruise fare paid for their May 24, 2013, Grandeur of the Seas sailing.
"Royal Caribbean International is deeply sorry for this unexpected development in our guests' vacation. We understand that this may have been a very stressful time for them. And we also know that it has significantly impacted their vacation experience.
"A dedicated telephone hotline has been established for family members of guests at 1-888-824-0012 or internationally at +1-408-916-9000. The cruise line requests that only families of guests use the telephone numbers in order to help ease call volume and ensure that they can receive information as quickly as possible."
