The 23-year-old Belgium international will not travel to Brazil after being ruled out of action for "a minimum of six months"
The 23-year-old suffered the injury during training and a scan on Thursday confirmed the extent of the damage, which the club say will sideline him for "a minimum of six months".
"It's a terrible blow both for Christian and for the club," boss Paul Lambert told the club's official website.
"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."
Benteke was a revelation in his first season in England, scoring 28 goals in 50 appearances for Villa and Belgium to help his club preserve their Premier League status and his country reach Brazil.
At the end of his first year the Belgian submitted a transfer request amid interest from Tottenham, before changing his mind and signing a new contract which keeps him at Villa until the summer of 2017.
His second season has been more problematic, yielding just 11 goals in 29 games, but Benteke was still set to battle Everton loanee Romelu Lukaku for a starting spot up front for Belgium this summer.
The injury is also a significant blow for Lambert as he bids to keep Villa in the top flight, though his side lie 12th in the table, eight points clear of 18th-placed Cardiff with a game in hand.