The Saints are already without outside linebacker Victor Butler, who has a torn ACL.
Wilson was injured when he tried to make a tackle in the backfield.
Though the reported timetable for a return would have Wilson back by Week 1, he will miss valuable time in training camp as the Saints install their new 3-4 defensive scheme under coordinator Rob Ryan.
"Right now, we will see where he is at. We said the next guy would be up. I don't anticipate it being a real significant injury," Saints coach Sean Payton said Monday.
Wilson, 24, had 19 tackles, three sacks and a forced fumble for the Saints in 2012, his second season in the NFL.
Information from The Associated Press was used in this report.