The 23-year-old was injured in Ghana's World Cup play-off win over Egypt and will now miss his side's remaining matches in 2013 - including the Champions League trip to Arsenal
The Ghana international suffered the injury during his country's World Cup play-off second-leg clash with Egypt in Cairo and was substituted in the 58th minute of last week's match.
On his return to France the 23-year-old underwent tests that diagnosed a problem with the lateral meniscus in his left knee that required an operation.
That operation took place on Monday and the club confirmed Ayew would not play again until 2014.
"Andre Ayew has been operated on successfully," a statement on the club's official website read.
"Andre will leave hospital tomorrow and his unavailability is estimated at about two months."
Ayew has scored four goals in 14 appearances for Marseille this season and was part of the Ghana side that qualified for Brazil 2014 with a 7-3 aggregate win.
He will now miss his side's remaining Ligue 1 matches this year with Montpellier, Lille, Nantes, Olympique Lyonnais, Toulouse and Bordeaux, as well as crucial Champions League clashes with Arsenal this Tuesday and Borussia Dortmund in December.