Scans showed the severity of the promising forward's injury, suffered in the recent 2-1 defeat at Stoke, and he will be operated on next week before beginning his rehabilitation.
"It's very disappointing for Callum, after what has been an exceptional start to the season, but I am sure he will come back fitter and stronger," manager Eddie Howe told Bournemouth's official club website.
"Callum is the type of character who won't be fazed by such a set-back, and I am sure he will turn this experience into a positive in the long run.
"As I have said many times before though, this kind of set-back offers others the opportunity to step up to the plate, show everybody what they can do and make a real impact at this level."
The loss of Wilson is the latest significant injury suffered by a Bournemouth player
It is possible the forward, who had scored five goals his previous six appearances before facing Stoke, will not return this season.
Club-record signing Tyrone Mings, who was recruited for Â£8million over the summer, will miss the remainder of the season with an anterior cruciate ligament injury, and with that same injury winger Max Gradel, a Â£7million summer signing, will also miss the next six months.
Source : PA