The German international picked up an injury while playing a friendly match against Lens last week.
On Per Mertesacker's condition, speaking to Arsenal's official website, manager Arsene Wenger said: "We have bad news on Per Mertesacker. He played in Lens on Friday night, he finished the game and had a little pain on his knee.
"We found out the next day that it was much more serious than expected. He had surgery yesterday in Germany.
"It all went well. I know you will ask me for how long he will be out. I don't know that, it's [some] months, but I don't know [exactly] how long he will be out for.
Mertesacker's injury comes as a huge blow for the Gunners who have dearth of quality defenders in their squad.
Wenger had planned of making the German the next club captain and was planning to buy a young defender as a cover for Laurent Koscielny and Mertesacker.
Laurent Koscielny is on an extended break due to his participation at the Euro 2016. The Gunners had planned to loan out Calum Chambers, but in the current situation they have to drop the plan.
It has been a frustrating transfer window for Arsenal so far as they have faced snubbing twice for Jamie Vardy and Alexandre Lacazette. The only signing they have completed is of Swiss international Granit Xhaka.