The Russian Premier League did not say whether the cases had been recorded among players or team staff.
Sochi, currently 12th in the 16-team league, had been scheduled to play 14th-placed Tambov on Thursday.
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The Russian Premier League resumed the season last month after having halted action in mid-March to contain the virus. A few matches have since been cancelled after outbreaks were reported at certain clubs.
Russia has recorded 752,797 cases of the virus, the fourth highest in the world.
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