Manager Paul Lambert confirmed the striker's injury, suffered during the weekend win over Norwich, following Tuesday night's 4-0 Capital One Cup defeat to Tottenham.
But while the Belgium international is set to miss at least a month, it is a prognosis that is not as bad as first suggested.
Villa were well beaten on Tuesday night in Benteke's absence, with summer signing Libor Kozak - who scored the winner at Norwich - handed a start in his place.
Following the news, Lambert said: "It is not as bad as we feared it was going to be. Maybe four, five, six weeks or so.
"The medical people give you the best and worst case scenario. You are never quite sure until you hear from the professor.
"Thankfully it is not too serious. It has got a lot better and he is feeling a lot better and the international break certainly helps us."