The French boss confirmed the injury to his defender in a press conference on the club’s pre-season tour.
The 31-year-old suffered the injury in Friday’s pre-season draw with Lens and did not travel with the rest of Arsenal’s squad for their two-match tour of the United States.
The German World Cup winner, who lost his place in the Gunners’ side towards the end of last season, will now miss the start of the new campaign.
It comes as a blow to the club and especially to Mertesacker – reports last week claimed the German was set to be handed the captain’s armband at the north London club.
Fellow central defender Gabriel was also left at home and, with Laurent Koscielny on an extended break following his exertions with France at Euro 2016, it means new signing Rob Holding is likely to be involved in both matches.
Wenger’s men meet the MLS All-Stars in San Jose on Friday before ending their short stint in the States with a game against Chivas de Guadalajara.
Mertesacker, who joined Arsenal from Werder Bremen in 2011, had captained the side on occasion last season before he was dropped as Wenger preferred to partner Gabriel and Koscielny at the heart of his defence.
England Under-21 international Holding was signed from Bolton earlier in the week but the 20-year-old, named the Trotters’ player of the season last year as they were relegated from the Sky Bet Championship, could now play a major part in the build-up to Arsenal’s season.
He could be paired with Calum Chambers against the All-Stars team, with the pair familiar with one another having been part of the England Under-21 squad which won the Toulon Tournament in May.
Wenger also confirmed another new signing, Switzerland midfielder Granit Xhaka, will play some part against the All-Stars following his big-money move from Borussia Monchengladbach earlier in the summer.