Clichy suffers suspected stress fracture
"We have lost Gael Clichy with a back injury," Wenger told a news conference on the eve of Wednesday's Champions League match against AZ Alkmaar.
"It looks like he could be out for a while.
"We fear a stress fracture but we will know more of that tonight. But if that is the case he will be out for a few weeks."
France play Ireland on November 14 in Dublin with the second leg in Paris four days later.
Kieran Gibbs will deputise against Alkmaar when victory would guarantee Arsenal's place in the Champions League knockout rounds.