The fire occurred Thursday while Splendour of the Seas was en route to Argostoli, Greece.
Though the fire was contained, 'in an abundance of caution, it was deemed necessary to evacuate some guests from their stateroom,' the company said.
Contrary to some media reports, there was no power loss.
Splendour of the Seas is sailing toward Venice, and all systems are functioning, Royal Caribbean said.
The ship is on a seven-night cruise that departed Venice on Oct. 17.