The 25-year-old was forced off after 32 minutes of Arsenal’s 3-0 Premier League victory over Chelsea on Saturday after coming off worse in a challenge with N’Golo Kante.
There were concerns that Coquelin could face a longer spell out of action, but Wenger expects him to be available mid-way through October after scans determined that the problem was not severe.
“Francis Coquelin is out for the game – it should be a short-term injury,” Wenger said ahead of Arsenal’s Champions League clash with Basel. “The scan was quite positive.”
When pressed for a time frame, Wenger replied: “It could be three weeks”.
The Gunners boss added that striker Olivier Giroud – banned for the Basel match – is a doubt for Sunday’s game with Burnley due to a toe injury.