Mertesacker suffered the injury in Arsenal’s 1-1 draw with Lens last Friday.
The German was left out of Arsenal’s touring party which left for the USA this afternoon.
Mertesacker was expected to be appointed Arsenal captain for the forthcoming season.
But the 31-year-old looks to have already got the Arsenal captain injury hoodoo, suffered by past captains Mikel Arteta and Thomas Vermaelen, before he has officially been given the job.
When Vermaelen and Arteta were given the captaincy roles full time, they both barely featured in the first-team due to injuries.
Gabriel has not travelled to the USA as he has tonsilitis.
New signing Rob Holding and Calum Chambers are Arsenal’s only other alternatives in the middle of defence.