The 26-year-old Paris Saint-Germain forward went to the airport in Belo Horizonte by helicopter, from where he was expected to head on a private jet to his luxury villa at the Mangaratiba beach resort around 100km from Rio de Janeiro.
According to Brazilian website Uol, Neymar's entourage have already prepared his recovery "headquarters" at his villa, which includes a gymnasium and a machine capable of producing 300kg of ice a day, similar to those used by modern football clubs.
The whole of Brazil is holding its breath while waiting to see if their star player, who captained the country to Olympic gold on home turf in 2016, would be fit to play in Russia.
But while Brazil frets over his potential World Cup availability, PSG are keen to get Neymar back playing before the end of the season, although he will miss Tuesday's crunch Champions League last 16 second leg at home to Real Madrid.
The world's most expensive player will not start training for at least another six weeks, the French doctor representing PSG at the Belo Horizonte hospital, Gerard Saillant, told journalists on Saturday.
- Champions League hope -
=========================
Should his recovery go well, Neymar could even be back in club action in May.
If PSG beat Real and then make it through the quarter-finals too, he might even be able to play in the Champions League semi-final second leg on May 1 or 2, or if not then perhaps the May 26 final in Kiev, Ukraine -- should the French outfit get that far.
And while Brazil scored a self-interest victory in ensuring Neymar underwent an immediate operation that PSG initially seemed reluctant to sanction, the French club are keen to regain some control over their player's recovery.
Brazilian surgeon Rodrigo Lasmar performed the operation, accompanied by Saillant, who previously operated on ex-Brazil star Ronaldo's injured knee.
Saillant, meanwhile, denied there was any conflict between the Brazilian football federation and PSG over their separate interests.
That was a reference to an article in French newspaper l'Equipe, which claimed that Lasmar had lied over the nature of the fracture to force Neymar to undergo surgery.
PSG had been hoping the forward would regain full fitness much sooner from what they considered a hairline fracture, whereas Brazil were keen to have him operated on to ensure he could recover and be fully fit by June.
Cocooned away in his homeland, Neymar appears to be ensuring Brazil continue to hold the upper hand in their arm-wrestle with PSG.
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