Russia’s Defence Ministry did not say how much damage the Ivan Khurs sustained in the attack it said was carried out by Ukrainian unmanned speedboats in the Black Sea.
It said the incident took place on the approach to the Bosporus Strait, which runs from the Black Sea through to the Mediterranean via Istanbul.
Moscow said that the ship was protecting the TurkStream and Blue Stream gas pipelines at the time of the attack but it "continues to fulfil its tasks".
TurkStream carries gas from Russia's Taman peninsula west across the width of the Black Sea to a point west of the Bosporus. Blue Stream, however, crosses the eastern Black Sea from north to south, making landfall more than 700 km east of the Bosporus.
Kyiv has not made any comment about the attack.
“All enemy boats were destroyed by fire from the standard armament of a Russian ship 140km north-east of the Bosporus,” Russian Defence Ministry posted on Telegram.
The Ivan Khurs is a reconnaissance vessel equipped with sophisticated radio and visual sensors as well as electronic warfare capabilities and is one of only two such ships in the Russian navy.
The ministry cited the attack as a justification for Russia expanding defensive measures. Explosions last September damaged the Nord Stream 1 and 2 pipelines bringing gas from Russia under the Baltic Sea to Germany.
The Russian statement appeared likely to raise tensions in the Black Sea, where Russia only agreed last week, one day before deadline, to extend a deal allowing Ukraine to export grain safely from its seaports.