The German defender sustained the injury during Arsenal's Premier League win at the Stadium of Light against Sunderland last weekend, putting his chances to feature for the Gunners over the remainder of the season in serious doubt.
"Unfortunately he has had surgery and we have lost him for a while," Wenger said. "How long I don't know. He had reconstruction of his ligaments. So it will be long term."
Mertesacker was sorely missed in Arsenal's midweek drubbing at the hands of AC Milan in Champions League play, as the Gunners were demolished, 4-0, at the San Siro.
Arsenal faces Sunderland in the FA Cup on Saturday and are also likely to be without Laurent Koscielny, who suffered a knee injury against Milan on Wednesday.