Boss Arsene Wenger said: "It is a big blow. Gael had a problem last season but on the other side of his vertebrae.
"It is a gradual thing. He could play pain-free but it got worse after games.
"We had a scan on Monday and saw he had a fracture. It will be between one month and two months."
It is a massive setback for the Gunners, coming just 24 hours after striker Nicklas Bendtner was ruled out for a month with a groin problem.