Prosecutors said on Friday that the investigation was opened following a complaint filed by the France-based International League Against Racism and Antisemitism (LICRA).
The 28-year-old singer is known worldwide for hits such as "Djadja", which has nearly a billion streams on YouTube alone.
The racist abuse follows reports that the singer discussed the possibility of performing a song by 20th century icon Edith Piaf during a meeting with President Emmanuel Macron last month. However, neither Macron nor Nakamura confirmed the reports.
At a campaign rally on Sunday organized by the far-right Reconquest party, led by former presidential candidate Eric Zemmour, Nakamura's name was booed by the crowd.
Right-wing extremist groups posted signs on the banks of the Seine saying, "No way, Aya. This is Paris, not the market in Bamako."
SOS Racism, another anti-discrimination group, said it had filed a formal complaint against the artist for "acts of incitement to discrimination and racist cyberbullying" on social media.
The statement said Nakamura was "the victim of waves of racist hatred driven by the far right." was stated to be.
Olympic organizing committee officials said on Monday they were "shocked" by the backlash against the singer.
Sports Minister Amelie Oudea-Castera also supported the singer on social media.
"Thank you for your support, especially my followers," Nakamura said on social media, adding, "I feel as if I made you discover Edith Piaf and she was reborn in me."
