The warship's task is to escort and protect Russian vessels or foreign ships with Russian crewmembers on board from pirate attacks off Somalia.
A Ukrainian ship, the Faina, carrying at least 33 tanks and other heavy weaponry, was hijacked in the region on September 25.
The Neustrashimy (Fearless) frigate is now in the Red Sea, and "is about to start fulfilling its role of maintaining the security of Russian shipping," Captain 1st rank Igor Dygalo said.
Dygalo said the Russian sailors would coordinate their activities with foreign warships now in the area to monitor the situation around the Faina.
"The ship will also fulfill a number of tasks in different maritime areas near the Horn of Africa with the U.S., France and other countries' vessels," Dygalo said.
The Russian captain of the Faina died of a heart attack after the vessel was seized. The pirates holding the ship have demanded an $8 million ransom, and have threatened to kill the hostages if a military operation is launched against them.
Pirates are increasingly active in the waters off Somalia, which has no effective government and no navy to police its coastline. Somali pirates have seized more than 30 ships so far this year off the coast of the east African nation.
Somali Ambassador to Russia Mohamed Handule said in early October his country had given permission for Russia's military to tackle pirates both off Somalia's coast and on its territory.
The Neustrashimy 's armament includes SS-N-25 Switchblade anti-ship missiles, SA-N-9 Gauntlet SAM, a 100-mm gun, torpedoes and depth charges. The frigate also carries a Ka-27 ASW helicopter.
The warship left the main naval base in Russia's Baltic exclave of Kaliningrad in late September and participated in joint drills with a Russian naval task force in the Mediterranean.