Wilshere sustained the injury after a training ground collision last week but the extent of the damage was only revealed Thursday.
Wenger says "I had a bad surprise because it is a hairline crack in his fibula" and that "there is minimal damage apart from bone damage."
The 23-year-old Wilshere, an England international, has had frequent injury problems throughout his career.
He missed five months of last season after surgery on a left ankle injury sustained against Manchester United in November.
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