The 30-year-old Spaniard was initially ruled out for "approximately three weeks" with a calf strain.
"Arteta's injury could be shorter than three weeks because it's a minor calf strain," Wenger told Arsenal's official website. "It's a light grade one so it could be quicker than three weeks.
"Mikel Arteta is an important player. First of all, he's a good player, a tactically intelligent player, and a winner. He has three important qualities that you miss when you don't have him."
Arteta joined Arsenal from Everton in 2011.