Walcott out for up to six weeks
The 21-year-old was hurt in the build-up to Wayne Rooney's opening goal in the 3-1 victory over Switzerland in Euro 2012 qualifying on Tuesday.
"The tackle looked quite bad," Wenger told the club's website. "Unfortunately it (his absence) will be four to six weeks.
"We had some good news about the scan because at some stage we were scared it could be worse. But overall it is a question of patience and rehabilitation."
Walcott, who began the season in fine form with four goals in his opening three matches for Arsenal, is now likely to miss Premier League games against Bolton Wanderers, Sunderland, West Bromwich Albion and Chelsea.
He is also likely to sit out Champions League ties against Braga and Partizan Belgrade and is a doubt for England's next Euro 2012 qualifier against Montenegro on October 12.