Cech suffered a calf injury as he raced back towards his own penalty area after coming up for a corner in the last minute of his side's 2-1 home defeat to Swansea on Thursday, a result which leaves the Gunners six points behind leaders Leicester.
Wenger, whose Arsenal side face their second-placed north London rivals Tottenham this weekend, confirmed the prognosis at his press conference.
''(He will be out for) three to four weeks,'' the Frenchman 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.''
Wenger went on to explain that Cech had a groin issue before the game but trusted him to play only to see his first-choice goalkeeper pick up a different injury.
The same happened with Alexis Sanchez earlier in the season when Wenger played him against Norwich despite knowing of a hamstring problem which then flared up in the game and ruled him out for the festive period.
''We had to make the decision before the game because he had a little groin problem but he declared himself 100 per cent fit,'' he said.
''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.''
Ospina will deputise for Cech at Spurs and in the coming weeks - with an FA Cup replay at Hull and a Champions League tie in Barcelona to come as well as league games against Everton and Watford.
The Colombia international came in for criticism after a big mistake in the Champions League defeat to Olympiacos earlier this season but Wenger has backed his man to step up now he is needed.
''I have complete confidence in David and I'm not worried at all on that front,'' he added.
Following the damaging defeat to Swansea, Wenger has been left to dispel criticism from Arsenal's record goalscorer Thierry Henry and also disagree with current star Sanchez - who said his side sometimes lack the hunger to win the Premier League title.
Ahead of their trip to Spurs, Henry - who works as an academy coach at Arsenal - told The Sun: 'I have never heard the Arsenal supporters as angry as they were at the Emirates on Wednesday night.
'They were less patient than I have ever known, booed one of the manager's substitutions and groaned every time a pass went astray or a tackle was lost.'
Wenger, who disregarded earlier criticisms from Henry's Sky Sports colleague Graeme Souness and another ex-Gunner in Paul Merson after a loss at Old Trafford on Sunday, was quick to respond to Henry's comments.
"Thierry Henry has his opinions," he said.
"He has not found the measurement of the fans' angriness, of 60,000 people straight away, because he sits in the best seats of the stadium."
Arsenal have now lost their last three games in all competitions and have not lost four in a row since 2002, where a late goal from Wayne Rooney saw Everton start that winless run, but Sanchez has risked rocking the boat having suggested in an interview with Directv that: "Sometimes we lack this hunger to believe that we can be champions."
"You have to take these comments a bit into perspective," Wenger said.
"I think that's always what's coming out. I believe that belief comes with the last results that you have made. Maybe our confidence has been a bit jaded but it's like always in football.
"We do 98 per cent of things right and we have to add the two per cent of things that are down to maybe finding back our collective qualities and even put more effort in.
"I don't see that (a lack of belief). I feel a massive disappointment after Wednesday's game."
That disappointment could peak with defeat at White Hart Lane, as Wenger also has to deal without defender Laurent Koscielny who is missing with his own calf complaint.