Adm. Vladimir Vysotsky said the reason for the move was "the current developments off the Horn of Africa and the Gulf of Aden, where Somali pirates have intensified their activity."
The U.S. Defense Department said on Wednesday that there had been 95 piracy attacks reported in the region this year, 39 of which were successful.
"There are at least 18 ships being held by Somali pirates as we speak," Pentagon spokesman Geoff Morrell said. "I believe our count is that 330 mariners are being held hostage by these criminals. And they come from 25 nations across the world."
Secretary-General Ban Ki-moon said in his quarterly report to the UN Security Council on Wednesday that pirates were estimated to have received up to $30 million in ransoms this year.
In October, Russia sent the Neustrashimy (Fearless) missile frigate from the Northern Fleet to Somalia's coast to protect Russian vessels in the country's waters. The Russian warship has prevented the seizure of at least two foreign vessels in the area.
Russia's Navy chief said: "After Neustrashimy, Russia will be sending warships from other fleets to this region."
NATO and the EU have recently announced plans to increase their naval presence in the Gulf of Aden and will launch on December 8 a joint naval operation, dubbed Atalanta, against piracy near the Somali coast. The operation could involve up to 10 warships.
The UN Security Council is set to meet on Thursday to discuss a new resolution imposing a travel ban and asset freeze on Somalis and Somali companies and organizations that violate the arms embargo, support acts threatening peace, and hinder the delivery of humanitarian aid.
