The Russian defence ministry claims the crew have all been evacuated and the cause of the fire is being investigated.
A Ukrainian official earlier said the ship had been hit by two missiles but did not give any evidence for the claim.
The warship has led Russia's naval assault on Ukraine, making it an important symbolic and military target.
It gained notoriety after calling on Ukrainian border troops defending Snake Island in the Black Sea to surrender - to which they memorably radioed a message of refusal which loosely translates as "go to hell".
Russia's Moskva warship Alexey Pavlishak
Vladimir Putin Reuters
The Russian military has been dominant in the Black Sea since the annexation of Crimea in 2014.
The Mosvka was previously deployed by Moscow in the Syria conflict where it supplied Russian forces in the country with naval protection.
It carries over a dozen Vulkan anti-ship missiles and an array of anti-submarine and mine-torpedo weapons.
The news comes after the Kremlin reacted with fury to the suggestion that Finland and Sweden could join NATO.
Dmitry Medvedev, Deputy Chairman of the Security Council of Russia, said Moscow would "take measures in the Baltic" if the two states went ahead with the plans.