The Spainard missed his first Premier League game of the season as the Gunners lost 2-0 to Manchester City, with his manager not expecting him to return before the end of January
The midfielder was injured in training ahead of Sunday's 2-0 loss to Manchester City, with his manager ruling him out of action for the remainder of January.
Arsenal have a run of five games in 17 days, including a trip to Chelsea on January 20 and the visit of Liverpool on January 30.
"He has a scan on Monday. He will be out for approximately three weeks. It is a calf strain," Wenger told reporters.
The defeat to the Premier League champions marked the first league game Arteta has missed this season.