Cazorla sustained the problem during Spain's 2-2 draw with Chile last Tuesday and missed Arsenal's 3-1 victory at Sunderland in the Premier League on Saturday as a result.
Arsenal manager Arsene Wenger has now confirmed that the 28-year-old will be out of action until the middle of October.
"Cazorla has an ankle problem," the Frenchman said. "He will be out for a few weeks as well.
"I don't think he will play before the next international break."
Wenger also has injury concerns over striker Olivier Giroud after the striker was substituted in the closing minutes at the Stadium of Light.
The France international has scored in every Premier League game this season, with Wenger unsure how serious Giroud's knee problem is.
"That's my worry (that Giroud is injured)," he added. "We are very thin at the moment.
"It's a knee problem. He is the player at the moment who we cannot lose."
