Neymar vehemently denies the accusation, which has dominated headlines and dogged Brazil's preparations for the Latin American tournament starting June 14.
Here's what could happen next for the world's most expensive footballer.
Beyond the potential sporting consequences of missing Copa America, Neymar's image has taken a serious blow.
Shortly before the 27-year-old player was injured in the Brazil-Qatar friendly in Brasilia on Wednesday, his accuser told a Brazilian broadcaster that she had been the victim of "aggression together with rape."
Hours later a video circulated on social media showing the young woman hitting Neymar in a hotel room and accusing him of assaulting her the day before.
Sponsors are clearly worried. Mastercard has cancelled an advertising campaign starring Neymar that was to be broadcast during the Copa America, Spanish media reported. Nike expressed its "deep concern" on Monday.
"Only football can save him," Fox Sports commentator Paulo Vinicius Coelho told AFP.
"It's enough that he focuses on his game. He showed this season with PSG that he is still capable of playing great matches."
Few Brazilian football fans or commentators appear to believe Neymar faked his injury so he could pull out of the Copa America due to the rape allegation.
"I don't believe in a fake injury, for me the image clearly evokes a ruptured ankle ligament," Coelho said.
But the timing raised eyebrows, coming shortly after a senior Brazilian Football Confederation (CBF) official had publicly suggested Neymar would pull out of the tournament.
CBF vice president Francisco Noveletto was quoted by Brazilian media on Tuesday as saying he was willing to "bet" that Neymar would quit.
"He doesn't have the psychological condition to face the Copa America and journalists," Noveletto said.
That prompted CBF president Rogerio Caboclo to insist Wednesday -- for the second time this week -- that Neymar would play in the tournament despite the rape accusations.
While some social media users looked to conspiracy theories to explain Neymar's injury, most put the incident down to fate.
"Fate has brought a solution to a problem that neither (coach) Tite nor the CBF or Neymar himself had the courage to solve for the sake of the Brazilian team and especially the player -- to remove him from the eye of the storm," wrote a Twitter user.
Neymar is scheduled to return to the football field with PSG on August 3 for the Champions Trophy game against Rennes in Shenzhen, China.
But it is not clear if he will have physically recovered by then. It took Real Madrid youngster Vinicius Junior, who suffered a ruptured ankle ligament in March, two months to return to the game.
And there is also the chance Neymar could miss the match for a non-sporting reason as he faces police investigations stemming from the alleged rape.
"I ask myself why he has had so many physical hic-cups in recent years when he was injured very little early in his career," Coelho said, referring to the foot injuries that sidelined Neymar for several months this year and last season.
Rumors have circulated in recent weeks that Neymar could return to FC Barcelona, but his recurring injuries and tarnished image could put off the Catalan club where Neyar played from 2013 to 2017 before his record 222 million euro transfer to PSG.
Brazil's national coach Tite, who has described Neymar as "indispensable" to the national team, but also not "irreplaceable", is looking for a substitute.
Vinicius Junior or Lucas could be called up. Another alternative is Ajax Amsterdam's David Neres.