The London Fire Brigade said that “a small part of the ship was damaged by fire” and the historic vessel, which is sited in Greenwich, south east London, is open as usual to visitors.
Firefighters were called at just after 7.30am and four engines with 21 firefighters raced to the scene.
Station manager George Vost said: “Firefighters worked incredibly quickly to get this small fire under control and minimise damage.
“Crews carried out salvage work on the ship.”
The cause of the fire is under investigation.
The Cutty Sark was reopened by the Queen in April 2012, five years after it was ravaged by fire.
The 2007 fire was caused by an industrial vacuum cleaner that had been left switched on for two days while a conservation project was being carried out to repair Cutty Sark’s iron framework.
The ship’s masts, saloon and deckhouses had been removed and put into storage in Kent when the fire took hold.