According to a complaint filed with Sao Paolo police and reported by the UOL and GloboEsporte websites, the world's most expensive footballer is accused of "using violence to have sex with the victim without her consent."
"I am accused of rape, it's a big word, it's very strong, but that is what has happened," Neymar said in a seven-minute video posted on Instagram.
"It surprised me, it's a really ugly thing and a sad thing because anyone who knows me knows what kind of person I am and knows I would never do such a thing."
Neymar, 27, then showed what he said was a long series of WhatsApp messages with the woman, including topless photographs of her in bed.
He added:"These are intimate moments but it is necessary to make them public to prove that nothing really happened."
The unidentified woman, who lives in Brazil, allegedly met Neymar through Instagram, and after exchanging messages, the footballer invited her to visit him in Paris in mid-May.
According to the complaint, Neymar arrived at the hotel "apparently intoxicated," and the two chatted and exchanged "caresses."
But then "he became aggressive and used violence to have sex with the victim without her consent," the document said.
Neymar's father, who is also his agent, categorically denied the accusations in an interview with Brazilian broadcaster Bandeirantes.
"This is not true, he has never committed any crime," said Neymar Santos, arguing that his son was a victim of blackmail. "We have all the evidence and we already gave everything to the lawyers."
According to Neymar Santos, his son and the woman went on a date, but Neymar did not want to see her again. Since then, the woman has tried to extort money from the player and his family, he said.
"My son can be accused of many things, but I know what kind of man he is ... it's clear that this was a trap," he said, adding that the WhatsApp messages released by the player would exonerate him.
According to the media reports, the accuser was in Paris from May 15 to 17, but waited until last Friday to file the complaint in Brazil because she was "emotionally shaken."
Neymar, who was transferred to PSG from Barcelona in 2017, is currently in Brazil preparing for the Copa America, which takes place in the country from June 14 to July 7.
His 2018-2019 season with his club has been blighted by injury.
Sao Paulo's security secretariat would not provide a copy of the woman's complaint to AFP, confirming only that one had been filed but saying its contents were classified.
Another star of world football, Cristiano Ronaldo, is facing allegations he raped a US woman in Las Vegas in 2009. The Portugal and Juventus player strongly denies the accusations.