Alex out for three weeks
The Brazilian scored the second goal in Sunday's 2-0 victory over Arsenal that put his team four points clear at the top of the table with 18 points from seven games.
"The central defender underwent medical assessment on a thigh muscle injury sustained in the closing moments of Sunday's win over Arsenal," the club said on its website.
"It is estimated he will be out for three weeks."
He has been ruled out of Brazil's friendlies against Iran on Thursday and Ukraine four days later and is also likely to miss Chelsea's Champions League match at Spartak Moscow and Premier League matches against Aston Villa and Wolverhampton Wanderers.