The Ghana international suffered the injury during his country's FIFA 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 the new year.
"Andre Ayew has been operated on successfully," a statement on the club's official website read.
"The player will leave hospital tomorrow.
"Andre's 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.
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