A small part of deck three and the hull timbers were damaged, however firefighters managed to contain the blaze, London Fire Brigade said.
Twenty firefighters were called to the ship in Greenwich, south-east London early today and put the fire out within an hour.
In 2007, damage that cost 10 million pounds to repair was caused by a blaze while the ship was undergoing a 25-million- pound restoration.
Fortunately, the ship's masts, saloon and deckhouses had already been taken off before the fire broke out in 2007.
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The fire in 2007 was caused by an industrial vacuum cleaner that was left on for two days.
An investigation has now been launched to find the cause of the latest fire, the BBC reported.
The visitor attraction has opened as usual today, the report said.
Built in 1869 for the Jock Willis Shipping Line, Cutty Sark was one of the last tea clippers to be built and one of the fastest, coming at the end of a long period of design development which halted as sailing ships gave way to steam propulsion. It was designed to carry tea from China to Britain.