كتب : وكالات
The 28-year-old Brazilian sustained the injury during training, Chelsea said on their official website on Thursday.
Chelsea goalkeeper Petr Cech also faces a month on the sidelines after suffering a calf injury on Wednesday.
Israeli winger Yossi Benayoun, who joined Chelsea from Liverpool, is also struggling with a groin complaint.
Chelsea, who won the domestic double last season, face Manchester United in the Community Shield on August 8.
They open their Premier League campaign against West Bromwich six days later.