The 25-year-old Antonelli died after being taken to the circuit's medical centre, it added.
Officials called off the race, and the day's headline World Superbike Championship event.
Russia's federal investigative committee was looking into the accident, the Russian Itar-Tass news agency reported.
(Reporting by Gabriela Baczynska in Moscow and Clare Fallon in London; Editing by Toby Davis)
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