Both Russians and Ukrainians claimed responsibility for the damage to the Russian missile cruiser in the Black Sea.
The Defense Ministry of Russia said that the Moskva had exploded due to a fire, and that the crew had been evacuated.
Odesa is a port city on the Black Sea in the south and the regional administrator wrote on his Telegram channel that the vessel had been hit with anti-ship missiles.
The claims have not been independently verified.
The Russian Black Sea fleet drew global attention in February after an audio exchange between the ship and border guards went viral.
The cruiser is the second Russian vessel to have sustained major damage since the beginning of the invasion.
On March 24, the Ukrainian navy said it had damaged a large paratroop ship in the Black Sea.