Scans confirmed a ruptured anterior cruciate ligament in his right knee, sustained during Saturday's 2-1 defeat at Stoke City, and the striker will have an operation next week.
"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 said.
"Callum is the type of character who won’t be fazed by such a setback, 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 setback offers others the opportunity to step up to the plate, show everybody what they can do and make a real impact at this level."
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Wilson, who joined the club from Coventry City in 2014, was top scorer last season with 20 goals as Bournemouth won the Championship (second tier) title.
He had begun the new season in excellent form, with five goals in seven games, including a hat-trick away to West Ham United.
Last weekend's defeat left the south coast club 16th in the table. Their next game is at home to Watford on Saturday.
(Reporting by Steve Tongue)
