Arteta sustained an ankle injury during Monday's 2-1 defeat to Wigan, and Wenger said afterwards that he feared the problem was "quite a serious one".
Scans confirmed that there was no break but the midfielder will not be available for the club's final four games of the season.
"It is season over for him, but he doesn't need surgery, which is what we were scared of, so he will be out for six to eight weeks," Wenger told Arsenal Player. "It is an ankle problem, but just a sprain."
Arsenal are currently third in the table, five points clear of Tottenham and Newcastle, though their Champions League rivals all have a game in hand.
They take on Chelsea this weekend and, while the recent defeats to QPR and Wigan have been disappointing, Wenger is delighted that the Gunners are in third place after such a poor start to the season.
"After losing four games in the first seven, to be where we are today is a remarkable achievement," he said. "Now our target must be to better what we did last season.
"A strong finish will be important for that reason, and also to give us the belief to enter 2012-2013 with confidence."
Gervinho added on Arsenal Player: "We want to be among the top three. The whole group is very motivated and we are already happy to be where we are.
"We can still do better with the four matches coming. We are fighting only for third place, we don't think about fourth spot. Everybody is determined to fight until the end, from the players and the manager to the fans, to maintain third place.
"If we manage to keep it then everybody should be proud because we fought very hard for it."