The Gunners shot-stopper pulled up with a hamstring injury in the recent 2-0 win against Watford after going down following a goal kick.
He was immediately replaced by Leno between the sticks, who made a number of key saves as he kept a clean sheet on his Premier League debut.
Ahead of Arsenal's Europa League clash against Qarabag in the Europa League on Thursday, the medical team have confirmed Cech will be out of action.
A statement from the club doctors said of his situation: "Left hamstring injury. Expected to return to full training in 3-4 weeks."
Leno will be looking to stake his claim at being the first-choice goalkeeper at the Emirates, after impressing in his three games for the North London side.
Leno recently revealed the words of advice he received from boss Unai Emery as he bided his time on the bench.
The 26-year-old said: "It’s difficult to sit on the bench but the coach said to me ‘Don’t be sad or disappointed, just train hard'.
“He has worked with many goalkeepers and it is a specialist position – it takes a little bit more time to build confidence and to get a feeling for the team."
Before adding: "Now Petr is injured, I have the opportunity to play more games and show the coach my quality.
“Some weeks ago he told me to stay calm because I played for just one professional club in Germany and it is a new country, a new language, and everything is new for me.”
The Arsenal medical team have also given updates on a number of other players, as they revealed that skipper Laurent Koscienly is in line to return to full training in November.
While Ainsley Maitland-Niles – who suffered a broken leg in the season opener against Manchester City – is well ahead of schedule.
The versatile youngster was due to be back in training in November, but will instead be back with the first team squad early this month.
Greek defender Dinos Mavropanos is also nearing a return back to action following his groin injury.
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