The Czech veteran could miss up to a month through injury.
The former Chelsea stopper suffered the problem late on in Wednesday's 2-1 home defeat to Swansea City when he ran up for a last-minute corner.
"Cech will be three or four weeks with a calf injury. 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," Wenger told Sky Sports.
"We had to make the decision before the game because he had a little groin problem but he declared himself 100 per cent fit. Then you have to trust the player. He's 33 years old and he knows his body. If he says he's fit then he is available.
"It is like it is. I focus on the future. You want the players to be tough enough to sometimes be able to play through a little pain. You're never completely perfect before a game in March."
He will definitely miss tomorrow's massive North London derby at Spurs, along with upcoming meetings with Hull, Barcelona, West Brom and Everton.
It is a major disappointment for the Gunners, whose title hopes hang by a thread and David Ospina will now deputise for the 33-year-old who, for the most part, had been in fine form this season.
It had been hoped that Cech - a four-time Premier League winner - could lend his wisdom to the less experienced Gunners on the title trail, but now he'll have to do so behind the scenes as the North Londoners continue to stutter.
They would have gone three points behind leaders Leicester City by beating Swansea, but it was a chanced missed for Wenger and co.