Cristiano Ronaldo, who also won the FIFA Men's Player of the Year award in October, added the 2017 Ballon d'Or to his previous wins in 2008, 2013, 2014 and 2016.
A tearful Neymar pleaded with the media to stop the "false stories" about his alleged frosty relations with PSG coach Unai Emery and fellow striker Edinson Cavani.
Neymar and Edinson Cavani reportedly fell out over penalty-taking duties after the Uruguayan refused to let the former take a spot-kick.
Neymar rolled in a 10th-minute spot-kick following consultation with the video assistant referee.
Neymar's representatives were not immediately available for comment.
Ronaldo is the overwhelming favourite to win the award, having led Real Madrid to the La Liga title and a third Champions League success in four years last season.
Brazil's media on Monday dubbed the spat between Paris Saint-Germain stars Neymar and Edinson Cavani over who should take a penalty kick during their victory against Lyon "a war of egos."
Kylian Mbappe was handed a starting spot on his debut after joining from Monaco on a season-long loan, with an option to buy for a fee that could reach 180 million euros (USD 216.5m).
In interviews with Catalan newspapers Mundo Deportivo and Sport, Bartomeu claimed Barca would be better off without Neymar this season following his world record 222 million euro ($263.7 million) move to Paris Saint-Germain.
PSG have already incurred sanctions for a previous violation and were slapped with a 60-million-euro fine, 40 million of which suspended, in 2014, and saw their squad for the Champions League cut from 25 to 21 players.
Neymar signed a new five-year deal with Barcelonain 2016, but the Catalans were powerless to stop his move to PSG just a year later as the French side met the buyout clause in his contract.
The people in charge at the Catalan giants "are not the people who should be there, for the direction of Barca," Neymar told reporters after scoring twice on his home debut as PSG thumped Toulouse 6-2 in Ligue 1 on Sunday.
Neymar had taken the place of Javier Pastore in the PSG side in the only change from last week's 2-0 win over Amiens.
Neymar is free to make his PSG debut at Guingamp on Sunday.
Josep Vives, a club spokesman, insisted Barcelona are unhappy with the way in which Neymar's exit came about.
Neymar denied that he was tired of playing second-fiddle to Lionel Messi at Barcelona.
The Brazilian left Barcelona for PSG for a 30 million Euro per year deal.
Neymar's world record move to Paris Saint-Germain was completed on Thursday when the French club confirmed the Brazilian superstar had signed a five year-deal