Zenit said on their website that the Russian international will have an operation to repair ligaments in his left knee in Germany on Friday.
Bystrov suffered the injury in the first half of Zenit's 3-2 win over Anzhi Makhachkala in a Russian Cup tie on Tuesday.
Zenit meet CSKA Moscow in the domestic Supercup, a curtain-raiser to the Russian league season, on Sunday and face Dutch side Twente Enschede in the Europa League last 16 tie later this month.
Zenit striker Alexander Kerzhakov will miss Sunday's match after falling ill last week and is doubtful for the Europa League first leg in Enschede.
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