The 26-year-old Tottenham Hotspur striker suffered the injury during Sunday's game against Hull City, limping off in the 39th minute as his side slumped to their fifth defeat in seven matches, the club's worst start to the season for almost a century.
Russia face Germany in Dortmund on October 11, and Finland in Moscow four days later.
The side has already lost Dynamo Moscow defender Denis Kolodin and Spartak Moscow midfielder Dmitry Torbinskiy to injury. Zenit striker Pavel Pogrebnyak, who missed his club's 8-1 win over Luch Energiya at the weekend, is expected to be fit for the games.
Russia began their 2010 World Cup qualifying campaign with a 2-1 win at home to Wales on September 10. Finland and Germany played out a thrilling 3-3 draw in Helsinki the same evening. The other teams in the group are Azerbaijan and Lichtenstein.
There are nine groups in total in the European qualifying zone. The first placed team in each group earns an automatic place at the 2010 World Cup, while the best eight second-placed teams will play off against each other.
The 2010 World Cup will take place in South Africa, the first time the tournament has been awarded to an African country.
