The Germany international was injured in Saturday's Premier League win at Sunderland and is poised to miss both legs of the last-16 tie with Milan as well as the North London derby against Tottenham Hotspur and his national team's friendly with France.
"He had reconstruction of his ankle in Germany before he joined us and the scan did not look too positive yesterday. Last night he went back to Germany to speak to the specialist and see where we go from there," Wenger told reporters on Tuesday.
"Certainly in the next month he will not be with us."
Arsenal and Milan are keen to show they have learned lessons from this stage last term with Wenger's men hoping to improve on the narrow defeat by Barcelona and the Italians wary of falling to another North London side after their loss to Spurs.
"It is a different competition now but we have the experience of it and we were very close to knocking Barcelona out last year," Wenger said. "I believe we have learned from that and it is a good opportunity to show that."
Milan, who included Alexandre Pato and Kevin-Prince Boateng in their squad after injuries, were determined to avoid the costly defensive slip-up of last season where they went out 1-0 on aggregate.
"We will have to pay great attention during the game, above all defensively, it's not a one-off game but played over 180 minutes," Milan boss Massimiliano Allegri told a news conference.
"Last year we made one mistake against Tottenham and look what happened. But we don't have an inferiority complex with English teams."
Wenger said the result of the tie would be a good gauge of how Serie A and the Premier League measured up to each other and pointed out that despite Arsenal's tendency towards youth and Milan's nod to older players, the clubs had a lot in common.
"Together we have a very balanced team," he joked. "Basically they have the same philosophy, that means they look after their players, they have a family attitude towards the way they treat the players, and we have exactly the same.
"They do it by keeping their players a bit longer and we have done it with some younger players but basically the philosophy is not so different."
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