Zenit said on their website that Semak would be out for four to six weeks after breaking his foot in a 2-1 win over CSKA Moscow in the Russian Supercup on Sunday.
"It's going to be very tough for us with so many injuries," said Italian coach Luciano Spalletti, who last year led Zenit to a domestic league and cup double in his first season in St Petersburg.
Winger Vladimir Bystrov will also be sidelined for at least six months after undergoing surgery to repair ligaments in his knee last week, while leading strikers Alexander Kerzhakov and Danko Lazovic are struggling to be fit for Sunday's league opener against Terek Grozny.
Zenit, who face Dutch side Twente Enschede in the Europa League last 16 later this month, said they wanted to sign a "top player" before the Russian transfer window closes on Friday.
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