Wenger also confirmed that the 21-year old will miss England's World Cup qualifying double-header against San Marino and Montenegro and will not recover for Saturday's game Premier League game against Swansea City.
Wilshere will be out for three more weeks and will not travel with his team to Bavaria as Arsenal look to overturn a 3-1 loss in the first leg.
"Jack Wilshere is out," Wenger said. "He has an inflamed ankle, the other ankle to one he injured. He will be out for three weeks and will not be available for Munich, Swansea and not for England."
"Hopefully for the Premier League he will miss only one game. After there is an international break. We can slowly prepare him," he added.
Wilshere played nearly 30 games having recovered after 17 months with a major ankle injury and Wenger feels this period would give him a much needed break.
"We trust people who are specialists in this area. He was out for 17 months and we had to deal with it, we must be able to deal with it for two or three games," he said.
Wenger has other injury concerns to deal with Bacary Sagna out with a knee injury and Kieran Gibbs, who has missed six weeks with a injury, is yet to recover. With Nacho Monreal cup-tied, Wenger will short of options at the back against Bayern.
However, Arsenal have some goods news ahead of their Champions League clash. Bayern will miss winger Frank Ribery with an akle problem while midfielder Bastian Schweinsteiger and Jerome Boateng are suspended.