The 26-year-old, who recently injured his hip whilst on international duty with France, was substituted just 17 minutes into the Gunner's 2-1 defeat at home to Chelsea on Saturday.
“It’s a thigh strain," Wenger told Sky Sports. "How bad? It’s minimum three weeks.”
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As for the match, Wenger felt his side had done enough to win after limiting Chelsea to just three shots on target and creating plenty themselves.
“I believe we were a bit nervous at the start and, after the first 20 minutes when we got into the game, we should never have lost,” the Arsenal boss continued.
“We played against a good team but we gave the game away. They had three shots on target and scored two goals.
“At set-pieces and defensively we were just not at the level you need in a big game like that, and that’s where we were punished.”
But the Frenchman does not believe that the absence of Per Mertesacker, who was omitted from the side in favour of returning captain Thomas Vermaelen, was the reason for their poor defending.
“That was a decision we made based on the opposition we faced,” Wenger insisted. “You can say it was the wrong one, maybe, but I believe it’s a bit lowering of the quality of the players who played.
“They are all international players. If I did not play Koscielny or Vermaelen and we lost the game you would ask me the same question.”