The statue of Satyr Playing the Flute is one of the main artworks in the grounds of the Gatchina Palace Museum, one of Russia's top tourist attractions.
Officials have been told that it would cost more than £40,000 to remove the nail varnish because of the way it reacted with the marble.
Museum spokesman Kuzma Boholyubov told local media: "It is really galling because it probably only cost pennies for the small amount of nail varnish that was used, but it's going to cost a small fortune to clean it all off.
"The minimum charge from professional restorers is 2.5 million rubles (£41,420). But it could be much higher depending of the type of nail varnish that the vandals used."
He added that it had so far proved impossible to discover who was behind the stunt so the museum would have to shoulder the cost.
"One of the problems is that we have a real shortage of CCTV cameras around the grounds, and this needs to be rectified," he said.
"We could probably have installed as many as we needed for the money is going to take to clean the statue and restore it to its previous condition."
The Great Gatchina Palace was built between 1766-1781 in the town of Gatchina, in Russia's Leningrad Oblast.
It was the favourite place to stay of Russian Empress Catherine the Great, who liked it so much that she bought it in 1783 and gave it to her son, the future Emperor Paul I.Post published in: World News