The German sustained a knee ligament injury last week which has kept him from the club's pre-season tour of the USA while forcing him to undergo surgery to address the problem area.
Wenger revealed that Mertesacker will be out for a few months with some outlets indicating that perhaps the injury will see the towering centre-half sidelined for the remainder of 2016.
"We have bad news about Per," said Wenger. "He played against Lens (last week) and had a little pain but then we found out it was worse and he had surgery.
"I do not know how long he will be out but it is definitely going to be for a few months.
"We need cover. We play some young players on Thursday (against the MLS All-Stars) but with Per being out, we are now a little short and I will have to bring somebody in."
Arsenal are also without Laurent Koscielny, who is on an extended holiday following Euro2016, while Gabriel Paulista missed the US tour due to tonsillitis leaving only 21-year-old Calum Chambers and recent signing Rob Holding, 20, as the club's only recognised centre-backs.