This season Neymar has scored 29 goals in 30 appearances for PSG across all competitions, while he has provided 15 assists.
"The recovery time will depend on the player's evolution".
A spokesperson for the Brazilian football federation confirmed the operation was a success.
"He will be re-evaluated in around six weeks in order to specify a possible date when he can return to training".
Brazil team doctor Rodrigo Lasmar, right, and French doctor Gerard Saillant, representing PSG, speak after the surgery.
His recovery will be monitored by Brazil and PSG physiotherapist Rafael Martini, who has been working alongside Neymar since he started his career at Santos in Sao Paulo.
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On Thursday, Lasmar said the star player - whose transfer from Barcelona cost PSG a record €222 million (then Dh960m) last August - would need at least two and a half months, maybe three, to return.
Neymar will definitely miss PSG's make-or-break Champions League last 16 second leg against Real Madrid next Tuesday.
The report said that Neymar was initially found to have suffered a minor fracture and that PSG were shocked to hear Lasmar say on Thursday that it was a serious break requiring a longer than expected recuperation.
They said: "Neymar is already in his room".
PSG coach Unai Emery says the club are working hand in hand with Brazil to ensure Neymar has every opportunity to recover as quickly as possible from the operation and prepare properly for the tournament in Russian Federation.
The physician added, however, that he should be in "full form" by the time of the World Cup.