Alex added to Chelsea injury list
Brazilian Alex injured his thigh in pre-season training and will be out for a month, the Premier League and FA Cup double winners said on their website on Thursday.
Czech keeper Cech is expected to be out for a similar length of time after tearing a calf muscle in his right leg.
The pair seem certain to miss the opening league game of the season at home to promoted West Bromwich Albion, who are managed by former Chelsea midfielder Roberto Di Matteo, on August 14.
The Blues also announced on Thursday that vuvuzelas would be banned from Stamford Bridge this season.
"The decision has been made to ensure the continued enjoyment and safety of fans following consultation with the club's stakeholders, including fans' representatives who showed strong support for a ban," Chelsea said in a statement.