He made a bright start against Birmingham at the Emirates Stadium but required treatment following a robust challenge by Liam Ridgewell and, despite returning to the field, was soon forced to make way.
Walcott will play no part in Arsenal's Champions League fixture away to AZ Alkmaar on Tuesday and could miss games against West Ham, Liverpool in the Carling Cup, Tottenham, Alkmaar in the return fixture and Wolves.
The winger may also struggle to be fit for England's friendly against Brazil in Doha on 14 November.
"The fact that he says he felt a little unstable when he was running is not good news," Wenger said after Arsenal's 3-1 win against Birmingham.
"We don't know yet how much of his pain is down to the kick and how much is down to the fact he twisted his ligament."
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