Mertesacker suffered ligament damage during Saturday's 2-1 victory at Sunderland and could be sidelined for the rest of the season.
"Unfortunately he has had surgery and we have lost him for a while," Wenger told the club's official website, www.arsenal.com.
"How long I don't know. He had reconstruction of his ligaments, so it will be long term."
The news on Laurent Koscielny's knee problem was more encouraging with the Frenchman expected to be out for only one week.
"He had a scan Thursday and the news is quite good,'' said Wenger.
"He will be out for hopefully around a week. He will miss the Sunderland game, but he should be back for next week."
Gervinho has finished international duty at the African Nations Cup and is included in the squad for the Stadium of Light.
Defender Carl Jenkinson will soon return to training following his back problem.
Wenger also revealed that Kieran Gibbs suffered no setback at the San Siro after being out since October with a groin problem.
"Kieran played his first game in four months in Milan so of course it was a shock to go back to that level. But physically he's all right,'' said Wenger.
"Carl's back in full training on Monday. That's good news for us.''