The England international has been plagued by ankle problems during his career, and picked up a fresh complaint at the weekend after being sandwiched in a heavy challenge between Marouane Fellaini and Paddy McNair during the 2-1 defeat to Manchester United.
Ahead of Arsenal's UEFA Champions League clash with Borussia Dortmund, Arsenal manager Wenger was unable to say exactly how long the 22-year-old would be out for.
"I can't give you any timescale there," said Wenger. "He'll be out for a while.
"He has to see a specialist next week to see how long."
Wenger also revealed that Theo Walcott will miss the meeting with Dortmund due to a groin injury, while goalkeeper Wojciech Szczesny will also be absent after he hurt his hip in the build-up to United's first goal.
However, defender Laurent Koscielny is back in the squad after an Achilles problem, and Wenger is in a positive frame of mind ahead of Wednesday's game at the Emirates Stadium.
"It's an important game for us and we have a good dynamic in the team which gives us a good chance against Dortmund," he said.
"I see similarities between Arsenal and Dortmund. They have had many injuries at the start of the season too.
"I believe in what I do and I believe in my players, their quality and their spirit."
Arsenal require a point against Group D leaders Dortmund to be sure of qualifying for the last 16.
