A club statement on Thursday revealed the 23-year-old will miss at least six months of action due to the injury.
Benteke has been Villa's top scorer in the past two seasons after joining from Genk, with 10 Premier League goals this campaign coming on the back of 19 in the previous term.
After a barren spell of four months without a goal, he has returned to form of late, with six in his last 11 league appearances, but the news comes as a significant blow for Paul Lambert's side.
"It's a terrible blow both for Christian and for the club," the Scot said.
"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."
Currently lying 12th in the table, eight points clear of the bottom three, Lambert's side look safe from relegation, but Benteke's absence will be keenly felt by a side that has scored just 34 goals in 31 Premier League games.
His injury also leaves Belgium boss Marc Wilmots without a key player heading into the tournament in Brazil.
Benteke featured in seven of Belgium's qualifiers, scoring twice, though Wilmots can turn to the likes of Romelu Lukaku and Kevin Mirallas in attack.
