It said it had also destroyed a Russian S-300 anti-air battery in the region.
Reuters could not immediately verify the battlefield reports.
The strikes on Odesa drew condemnation from the United Nations, the European Union, the United States, Britain, Germany and Italy.
Russian news agencies quoted Russia's defence ministry as saying that an Ukrainian warship and U.S. supplied anti-ship missiles were destroyed.
"A docked Ukrainian warship and a warehouse with U.S.-supplied Harpoon anti-ship missiles were destroyed by long-range precision-guided naval missiles in Odesa seaport on the territory of a ship repair plant," it said.
On Saturday, Turkey's defence minister said Russian officials told Ankara that Moscow had "nothing to do" with the strikes.