Ukraine's navy declined to comment.
"The last warship of the Ukrainian navy, the Yuriy Olefirenko, was destroyed at a warship mooring in the port of Odesa," Russian Defence Ministry Spokesman Igor Konashenkov said in a daily briefing on the war.
He said the vessel had been hit with "high-precision weapons" - a phrase he uses to mean missiles - on May 29 but gave no further details.
Oleh Chalyk, a spokesman for the Ukrainian navy, said he would not respond to any assertions made by Russia.
The Ukrainian navy will not disclose any information about losses during the war, he added.
Ukrainian officials said on Monday that Russia had put five aircraft out of action in an attack on a military target in western Ukraine and caused a fire at the Black Sea port of Odesa in heavy air strikes early on Monday.
Reuters was unable to independently verify the battlefield accounts of either side.
The Russian defence ministry also said on Wednesday that its forces had pushed Ukrainian units out of positions around the settlements of Krasnohorivka and Yasynuvata in Ukraine's eastern Donetsk region.
The ministry said "fierce fighting" was continuing around Avdiivka, a large town located between the two settlements, which has been largely razed to the ground during months of fighting.
Russian-installed officials inside Ukraine said on Wednesday five people had been killed in Ukrainian army shelling of a Russian-occupied village in the east.
There was no immediate comment from Ukraine on the Russian reports, in a week when the two countries accused each other of spreading terror in their capitals with air strikes.
Thousands of civilians have been killed in Ukraine and towns and cities laid to waste since Russian forces invaded 15 months ago but Tuesday marked only the second time Moscow had come under direct fire - from a flurry of drones - although oil and military facilities elsewhere in Russia have been hit.
In the Russian town of Shebekino, two of four wounded people were hospitalised and shells damaged an apartment building, four homes and a school as well as power lines, regional governor Vyacheslav Gladkov said.
Gladkov said on Saturday that he had come under artillery fire when trying to enter the town, about 7km north of the border with Ukraine, and that two industrial facilities were hit there on Monday.
Both sides say they are targeting the build-up of each other's forces and military equipment ahead of Ukraine's counteroffensive, which it says will come in days or weeks, to try to drive Russian forces out of its east and south.
Germany, once Russia's biggest energy market, reiterated that it deemed such Ukrainian attacks on Russian soil legitimate in terms of international law, and announced a sharp downgrading of diplomatic representation in both Russia and Germany.
Russian-installed officials in Ukraine's eastern Luhansk region said Ukraine had killed five people and wounding 19 in a rocket attack on a farm in the village of Karpaty.
Drones attacked two oil refineries 65-80km east of Russia's biggest oil export terminals on Wednesday, according to Russian officials, who did not attribute blame.
They said a fire at one of the terminals was later put out.
International Atomic Energy Agency chief Rafael Grossi laid out five principles at a United Nations Security Council meeting on Tuesday to try to safeguard the Russian-held Zaporizhzhia nuclear power plant in southern Ukraine.
Neither Russia nor Ukraine committed to respect them.
