The report, published on the Telegram messaging app by state television reporter Alexander Sladkov, did not say precisely when and where Major General Roman Kutuzov was killed.
There was no immediate comment from the Russian defence ministry.
Russian forces have intensified attacks to capture Sievierodonetsk, a key city in Ukraine's eastern Donbas region that Moscow is targeting after failing to take the capital Kyiv early in the war.
Russia already classifies military deaths as state secrets even in times of peace and has not updated its official casualty figures in
Ukraine since March 25, when it said that 1,351 Russian soldiers had been killed since the start of its military campaign on Feb. 24.
Russia says it is carrying out "special military operation" designed to demilitarise Ukraine and rid it of nationalists threatening the Russian-speaking population. Ukraine and Western countries dismiss Russia's claims as a pretext to invade.
Britain's defence ministry said on Monday that Russia appeared to have suffered significant losses amongst mid- and junior-ranking officers in Ukraine.
(Reporting by Reuters; editing by Guy Faulconbridge and Nick Zieminski)
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