Wilshere, 22, damaged ankle ligaments in a tackle by Paddy McNair during Arsenal's 2-1 loss at home to Manchester United in the Premier League last weekend and underwent surgery on Thursday.
He previously spent 17 months on the sidelines after sustaining a stress fracture of the other ankle in July 2011, but Wenger believes he has sufficient strength of character to overcome his latest setback.
"He is very down
Jack is a football man who loves the game, but on the other hand, he is a very strong character as well and he has learnt to deal with adversity from a very young age," said Wenger.
"I think he will be back at the end of February, beginning of March, and he will focus on coming back to rehab, having a strong rehab, and then I am sure he will help us to do well until the end of the season.
"Jack always came out stronger and, when I spoke with him, the final sprint of the season is already in his mind and (he wants) to come back stronger."
Meanwhile, Wilshere took to photo-sharing website Instagram on Friday to dispute an assertion by British newspaper Daily Mirror that he had "brittle ankles".
Alongside a photograph of McNair's challenge, which shows Wilshere's left ankle being twisted at an unnatural angle, he wrote: "As this picture clearly shows most people/players would have broken their ankle if someone tackled them like this.
"Luckily I have 'loose joints', not brittle' and only damaged ligaments."
Wenger said that McNair's challenge, which went unpunished, was "very bad", but accepted that it was "not malicious".
He said: "When you see it again, I don't think that anybody would have escaped without surgery in this tackle."
Wilshere is the latest in a long list of Arsenal players to have succumbed to injury and Wenger said that he would look to bring in "at least one body" during the January transfer window to bolster his squad.
However, he denied press reports that he is interested in signing out-of-favour Chelsea goalkeeper Petr Cech and said there had been "no enquiry from anybody" for unsettled Germany forward Lukas Podolski.
Source : AFP
Source: AFP