The Czech Republic international sustained the knock when he raced back towards his own goal after going up for a corner in his side's 2-1 home loss to Swansea City on Wednesday.
"(He will be out for) three to four weeks," Wenger said.
"It is not more serious. It is a serious calf injury and he had a groin alert on the first goal and he could not kick the ball properly out because of his groin and maybe compensated a little too much and provoked another muscular injury."
Arsenal, who trail log leaders Leicester City by six points with 10 games left, next host title rivals Tottenham Hotspur at White Hart Lane on Saturday.
David Ospina will deputise for Cech against Spurs, and is expected to continue in goal in a FA Cup replay at Hull and a Champions League tie with Barcelona. Wenger's charges are also set to face Everton and Watford in the league in the coming weeks.