The 27-year-old required reconstructive surgery on his ankle after picking up the injury in Saturday’s 2-1 Premier League win over Sunderland last Saturday.
“Unfortunately he has had surgery and we have lost him for a while,” Wenger told reporters.
“How long I don’t know. He had reconstruction of his ligaments. So it will be long term.”
Arsenal will return to the Stadium of Light on Saturday for their FA Cup fifth-round tie against Sunderland and Wenger will also be without defender Laurent Koscielny who is recovering from a knee injury.
“[Koscielny] had a scan yesterday and the news is quite good,” Wenger said. “He will be out for hopefully around a week. He will miss the Sunderland game. But he should be back for next week.
“[Gervinho] is back in the squad. From the other night, we have lost Koscielny. Everyone else is available for selection.”
Arsenal will be looking to bounce back against Sunderland following a 4-0 defeat at AC Milan on Wednesday. Kieran Gibbs featured at left-back at San Siro, and Wenger conceded the defender needed to acclimatise quickly in his return.
“He played his first game in four months in Milan," said Wenger.
“So of course it was a shock to go back to that level. But physically, he is all right.”
“[Carl Jenkinson is also] back in full training on Monday. That is good news for us.”