The goalkeeper was hurt sprinting back from a late corner kick and is set to miss the north London derby clash with Tottenham, along with defender Laurent Koscielny
Wenger will be without both Cech and Laurent Koscielny for the north London derby against Tottenham on Saturday.
But the Gunners boss has now revealed the former Chelsea man has a "serious calf injury" and will be out for three to four weeks, after aggravating a previous problem whilst running back from a late corner against the Swans.
Koscielny, meanwhile, continues to recover from a "small injury", having missed the 2-1 defeat to Swansea with a separate calf problem.
"It’s a serious calf injury," Wenger told reporters. "He [Cech] had a groin alert and maybe compensated a bit too much and provoked another muscular injury.
"The problem we had to decide was before the game, but he declared himself 100 per cent fit. You have to trust the player - he’s 33 years old and a professional.
"You want the players to be tough enough sometimes to play with little pains because players are never perfect in March.
"Koscielny is a small injury but he’s out for tomorrow, maybe Tuesday [against Hull City]. It’s a grade one [injury] so it’s a very short one. I don’t think he will be available on Tuesday but next Saturday he will be alright."
Wenger also issued an update on midfielder Jack Wilshere's recovery from the broken fibula that has seen him sidelined for the entirety of the 2015-16 campaign, with the Frenchman hopeful he will return in "three to four weeks".
READ MORE | Hodgson offers Wilshere hope
With Saturday's trip to Tottenham taking on even greater importance after both teams lost in midweek, many have speculated that a defeat for the Gunners could extinguish their title hopes.
However, Wenger maintains that he and his players are not taking any special measures to prepare for their visit to White Hart Lane.
"It is a big one, a very important one (but) the preparation is the same," he added. "We have a competitive rivalry but a fair one. You have that in sports.
"It is hard to predict what will happen tomorrow. It is one of the few derbies where the title is at stake."