According to a police source, cited by Nice-Matin, one soldier was wounded on the cheek, the second on the leg, and the third slightly on the chin.
The perpetrator was arrested, and the police found his identity papers in the name of Moussa Coulibaly, said le Figaro.
The soldiers were providing security protection, when they were attacked, as part of France's Vigipirate plan in front of a building housing the Jewish Consistory of Nice, Radio Shalom and Jewish association.
The anti-terrorism section of the Nice prosecutor office has begun an investigation.
Meanwhile, Christian Estrosi, mayor of Nice, confirmed a total of two suspects were arrested after three soldiers were attacked, said Tuesday BFMTV.