The 19-year-old suffered a hip injury just nine minutes after coming on as a substitute in the second half of the Gunners' 1-0 defeat to Norwich City in the Premier League on Saturday.
"It was a kick on his hip," Wenger told ESPN. "It is not long-term but he will be out for Wednesday."
"I don't see anyone new being [back] for Wednesday night," said the Frenchman.
"The closest will be Gibbs but he will not be ready. [Theo] Walcott will not be ready [either]."
Arsenal have won both of their Group B matches in the Champions League so far.