Alex is out for a month and will miss Friday's friendly trip to Ajax along with new signing Yossi Benayoun, who has a groin problem.
"There are no more coming that didn't play against Crystal Palace, so Yossi Benayoun is out and Alex has a problem in his thigh but with the other players it is the same squad," said Carlo Ancelotti on Chelsea's website.
It is the second such blow in successive days for the Blues, who yesterday saw goalkeeper Petr Cech ruled out for a month with a torn calf.
Tomorrow's game will therefore give back-up keepers Hilario and Ross Turnbull the chance to stake a claim to begin the season in the first team.
"I think that against Ajax we will play 45 minutes each for Turnbull and Hilario, and I think Turnbull will start the game," Ancelotti said.