The investigation is being led by the prosecutor's office in the Paris suburb of Nanterre, the official said.
A judicial source told ESPN on Monday that a 23-year-old woman went to police over the weekend and said that Hakimi, 24, raped her. The woman didn't want to press charges, but the prosecutor's office still decided to open an investigation, the ESPN source added.
PSG officials did not respond to requests for comment, and Hakimi has not publicly responded to the accusation.
ESPN reporter Julien Laurens contributed to this story.