Priazovye left Russia’s naval base in the Ukrainian Black Sea port of Sevastopol late on Sunday, Interfax quoted an unidentified Russian military source as saying.
The reconnaissance vessel would be operating separately from a navy unit permanently stationed in the Mediterranean, the report added.
Priazovye is on a mission that Russian President Vladimir Putin said is needed to protect national security interests, Interfax added.
The Russian Defense Ministry has made no comments so far.
Last week, Moscow said it plans to dispatch an anti-submarine ship and a missile cruiser to the Mediterranean.
The move by Russia comes at a time that the West is engaged in war rhetoric against Syria.
The call for military strike against Syria intensified after the Takfiri militants and the foreign-backed Syrian opposition accused the government of President Bashar al-Assad of launching a chemical attack on militant strongholds in the suburbs of Damascus on August 21.
The Syrian government categorically rejects the claims, syaing the attack was carried out by the militants to draw in military intervention.
US President Barack Obama delayed an imminent military strike against Syria on August 31 to seek approval for the move from the Congress, which will debate the issue when federal lawmakers return from recess on September 9.
The Obama administration has, however, said it “has the right” to attack Syria even if the Congress does not approve the measure.
