The Udaloy-class destroyer is part of a task force from Russia's Northern Fleet led by the Admiral Kuznetsov aircraft carrier, which is currently on its way to the Mediterranean.
Capt. 1st Rank Igor Dygalo said the visit will last until December 22.
Following the visit, the task force will pass through the Strait of Gibraltar, visit several ports in the Mediterranean, and participate in joint exercises with Russia's Black Sea Fleet.
Dygalo earlier said that Russia currently has three naval task groups on tours of duty in the world's oceans.
Another naval task force from the Northern Fleet, led by the Pyotr Veliky nuclear-powered missile cruiser, is currently on a tour of duty in the Caribbean.
The Admiral Chabanenko missile destroyer and two support ships from this task force sailed into Cuba's Havana Bay on a visit earlier on Friday which will last through December 23.
Meanwhile, a task force from Russia's Pacific Fleet, comprising the Admiral Vinogradov, an Udaloy class destroyer, a tugboat, and two fuel tankers, is in the South China Sea heading to the Indian Ocean to take part in the INDRA-2009 joint naval drills with the Indian Navy.
Russia announced last year that its navy had resumed and would build up a constant presence in different regions of the world's oceans.