Twenty nine-year-old Pogba has not played for the Serie A side this season since re-joining from Manchester United in the summer.
He suffered a knee injury in July and initially opted not to have surgery in a bid to be fit for the tournament.
France’s first World Cup match is against Australia on 22 November.
In a statement, Pogba’s agent Rafaela Pimenta said following medical review in Torino and Pittsburgh, it is extremely painful to inform PAUL Pogba will still need recovery time from his surgery.
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