Sao Paulo state's public security ministry released a statement confirming the accusation had been made, and said the investigation was still sealed, without giving further details. The police report was obtained by several news organisations including Reuters.
The accusation represents a fresh blow for the Brazilian, who has seen his international reputation suffer amid incidents of indiscipline.
Neymar posted a long video on his Instagram page, in which he denied all the accusations against him, claimed to be a victim of extortion, lamented the pain caused to him and his family, and shared WhatsApp messages with the alleged victim, including racy photos she sent him.
"I'm being accused of rape," he says in the video. "Whoever knows me, knows of my character and my nature, and knows that I would never do a thing like that ... What happened is exactly the opposite of what they're saying."
His representatives directed Reuters to their official statement, accusing a Sao Paulo lawyer purportedly representing the victim of trying to extort the soccer star. Reuters was unable to determine the identity of the lawyer or to seek comment on the extortion allegation.
"Faced with this unfortunate, illegal and outrageous event, we completely repudiate the unjust accusations and, above all, the exposure in the press of an extremely negative situation," the statement said. "All evidence of attempted extortion and non-rape shall be submitted to police in a timely manner."
Neymar's father, Neymar Sr., said earlier in a local TV interview that his son needed to move quickly to clean his name or risk the situation snowballing.
"If we have to show Neymar's WhatsApps and the conversations with this girl, we will, because it is clear that it was a trap," he said, adding they were living "difficult moments."
According to the police report, the unnamed woman told investigators in Sao Paulo that she met Neymar on Instagram and he suggested they meet in Paris, where he plays for Paris St Germain. Neymar's assistant sent her plane tickets and on May 15 she checked in to the Hotel Sofitel Paris Arc Du Triomphe, according to her account.
The Sofitel hotel did not immediately respond to a request for comment.
The woman told police that Neymar arrived at the hotel that night "apparently drunk," and that they talked and "caressed."
"However, at some point, Neymar became aggressive, and through violence, practiced sexual intercourse against the will of the victim," the police report says.
The woman told police she returned home to Brazil two days later without telling French police about the alleged rape because she was "emotionally shaken and afraid to register the facts in another country," according to the report.
Neymar is currently in Brazil, training with the national soccer team ahead of this month's Copa America.
Earlier in May, Neymar was banned for three matches by the French football authorities for hitting a fan after PSG's French Cup final loss to Rennes, and was also reportedly involved in a dressing room fracas with his PSG team mates.
Paris St Germain did not immediately respond to a request for comment. Brazil's football federation (CBF) declined to comment.
(Reporting by Leonardo Benassatto; Additional reporting by Julien Pretot and Sarah White in Paris; Writing by Gabriel Stargardter; Editing by Daniel Wallis, William Maclean)
