About 500 Spartak fans temporarily blocked Myasnitskaya Street.
From time to time, fans light pyrotechnics and throw firecrackers.
Several police squads are on duty nearby, TASS reports.
Spartak defeated Dynamo 2-1 in the final.
For Spartak, this was the fourth Cup won in Russian history.
Previously, the club won the tournament in the seasons - 1993/94, 1997/98 and 2002/03.
Earlier, the head coach of Spartak, Paolo Vanoli, shared his first emotions from winning the Russian Football Cup before the award ceremony.