The destroyer, the Marshal Shaposhnikov, freed a Russian tanker taken over by pirates in its first-anti-piracy mission in 2010, RIA Novosti reported Saturday.
The task force, which includes a tanker and rescue tug boats, is part of Russia's Pacific Fleet, said Capt. 1st Rank Roman Martov.
The Marshal Shaposhnikov carries two Ka-27 naval helicopters and a unit of naval infantry, Martov said.
En route, the task force will make an official visit to the Indian port of Mumbai and participate in joint drills with the Indian navy, the spokesman added.
Russia joined the international anti-piracy mission in 2008.
Megyn Kelly: Santa Claus and Jesus are both white men
Wisconsin business offering 'therapeutic cuddling' forced to close