The Trikand frigate carried out workup trials on March 14 and was cleared for final state trials on April 4, spokesman Sergei Mikhailov said, adding the trials will last through the end of April.
The frigate is due to be handed over to the Indian Navy this June, Mikhailov said.
Russia and India signed a $1.6 billion contract on the construction of three modified Krivak III class (also known as Talwar class) guided missile frigates for India in 2006.
The first frigate, INS Teg, joined the Indian Navy on April 27, 2012, and the second, The Tarkash, arrived at the port of Mumbai in India on December 30, 2012.
The frigates are each armed with eight BrahMos supersonic cruise missiles.
They are also equipped with a 100-mm gun, a Shtil surface-to-air missile system, two Kashtan air-defense gun/missile systems, two twin 533-mm torpedo launchers and an antisubmarine warfare (ASW) helicopter.