Pogba has been unable to feature for Juventus this season since rejoining from Manchester United on a free transfer.
The 29-year-old picked up a knee injury in pre-season but delayed a decision to have surgery on the problem.
He was pronounced doubtful for the World Cup when he finally decided to go under the knife but will now sit out France's trip to Qatar.
Pogba's agent Rafaela Pimenta said in a statement: "Following yesterday and today's medical review in Torino and Pittsburgh, it is extremely painful to inform Paul will still need recovery time from his surgery. For this reason, Paul will not be able to join the Juventus squad before the World Cup break nor the French National Team in Qatar.
"If wishful thinking would change things, Paul would be playing tomorrow. But what changes things are hard work, resilience and discipline, all of which are the only things in Paul's mind at these challenging times. Paul will continue working giving his very best to be back on the pitch for the fans and his team as soon as possible."
The injury represents another big blow to France manager Didier Deschamps, who has already been robbed off the services of Chelsea midfielder N'golo Kante for the upcoming tournament.
Pogba and Kante started the 2018 World Cup final in Russia when France defeated Croatia 4-2 to win the trophy for a second time.
Pogba has been capped 91 times by France, scoring 11 goals.
