The Brazilian injured himself against Marseille on February 25 and was forced to leave the field on stretcher, hinting that he may not be fit for the World Cup.
The 26-year-old has scored 28 goals in 30 appearances for PSG since joining from Barcelona for £200m last summer.
The Paris Saint-Germain player will begin his post-operation recovery at his mansion in Mangaratiba, along the southern coast of Rio de Janeiro state, local media reported.
"The operation, conducted by Doctor Rodrigo Lasmar, was successful. Neymar's injury will be assessed in six weeks' time to establish a possible date for his return to training".
The world's most expensive player was operated on by the Brazil national team doctor in Belo Horizonte to fix the fractured metatarsal and sprained ankle he suffered in last weekend's French league match against Olympique Marseille.
Lasmar pointed out that physiotherapy would be done by Rafael Martino, who does work both for PSG and the Brazilian national team, which "shows the integration of all parties". Earlier reports said he will be out for up to three months.
On March 6, PSG host Champions League holders Real Madrid, already trailing 3-1 from the first leg.
The physician added, however, that he should be in "full form" by the time of the World Cup.
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.
However, doctors stressed on Saturday that there was no friction between PSG and Brazil's federation, the CBF.