The Daily Mirror reported that the injury-prone England star has "a suspected hairline fracture in his left fibula (the smaller of the two bones that make up the lower leg), which would be yet another shattering blow", and the news was confirmed on Arsenal's website on Thursday.
"The information you have heard about Jack Wilshere is right,” Wenger told Arsenal.com.
"I had a bad surprise because it is a hairline crack in his fibula that makes him a few weeks out.
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"There is minimal damage apart from the bone damage - there is no damage at all apart from that. It was a collision in training and it was all completely accidental."
The injury was sustained in training ahead of the Community Shield match on Sunday, which Arsenal won 1-0. Gunners boss Arsene Wenger said at the time that Wilshere would only be out for "a matter of days", but that optimistic view proved premature.
Further scans showed that he will spend weeks out of action, though it seems that he will avoid surgery that would have seen him sidelined for three months.
As well as the blow to Arsenal - for whom Wilshere recaptured some of his best form at the end of last season - it is also a dent to England's Euro 2016 campaign, with the 23-year-old will miss the qualifiers against San Marino and Switzerland next month.
While England are near-certain to progress to the tournament in any case, it robs Roy Hodgson of the chance to start putting a settled first XI together with the tournament now just 10 months away.
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