"The Italian (Antonelli) rider died as a result of his injuries," a police official told the RIA Novosti news agency.
The source said that three riders had been involved in the accident.
Italian newspaper Gazzetta dello Sport said the accident happened on the first lap of the Supersport World Championship race as the 25-year-old Antonelli lost control of his Kawasaki and was hit by compatriot Lorenzo Zanetti.
Emergency services were quickly on the scene, according to Gazzetta, but Antonelli never regained consciousness.
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.
The Russian Grand Prix is the eighth event on the FIM Superbike World Championships calendar.