Aston Villa confirmed that he sustained the injury in training on Thursday and will undergo surgery after a scan revealed the extent of the injury.
He is expected to be on the sidelines for a minimum of six months.
"It's a terrible blow both for Christian and for the Club," said Villa manager Paul Lambert.
"He will miss the rest of the season, obviously, and also the World Cup. But he'll work hard because that's what he does and he'll come back for us stronger than ever next season."
News of Benteke's injury was first broken by Kristof Terreur, of Het Laatste Nieuws, a Dutch language newspaper based in Brussels, a series of tweets - even though Lambert made no mention of any injury to Benteke during his press conference earlier in the day.
After an indifferent start to the season, the Belgian striker has begun to pick up form in recent weeks with six goals in his last 11 matches.
He has six goals in 17 appearances for his national team, and has been a first choice striker for a side packed with talent including Eden Hazard, Romelu Lukaku, Kevin Mirallas and Marouane Fellaini.
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