The alleged rape took place May 15 in Paris.
The complainant said she flew from Brazil to France with the intention of meeting the international star after exchanging messages with him on Instagram. According to the report, the woman said Neymar met her at a hotel and was "drunk" and "aggressive" before forcibly having sex with her without consent.
The woman said she returned to Brazil two days later, upset and scared to speak out. She filed the report in Sao Paulo on Friday.
PSG has not commented on the report, but Neymar released an Instagram video stating his innocence.
Per ESPN.com, the video "included a long WhatsApp conversation he says he exchanged with the accuser in a friendly way days after the alleged incident."
Neymar also said the woman's accusation was "a setup." ESPN further wrote that Neymar said the woman was making "an attempt of extortion against him, echoing thoughts his father and agent expressed earlier Saturday on Brazilian television."
The 27-year-old just completed his second season with the French club, helping the squad win the Ligue 1 title in each year.
He has been in his home country to train with the Brazil national team, which is preparing for a friendly against Qatar and the upcoming Copa America later this month.