Eight-year-old Kenzo was invited to the match to meet the Marseille squad. His family were guests of Air Corsica and wore Marseille jerseys when spectators entered their box and "shamefully abused" them.
After the match, a France 3 TV journalist was attacked by Marseille supporters at a filling station near the stadium and was left needing hospital treatment. Prosecutors have opened an investigation into the incident.
"These individuals in no way represent the values of our club and our island," a club statement said. "Even the most extreme stupidity cannot excuse this behaviour. The club strongly condemns these unspeakable acts.
"AC Ajaccio will shed light on these shameful actions. As soon as the individuals have been identified by our services, we will file a complaint against them."
Kenzo's mother told local newspaper Corse Matin that the father was attacked and Kenzo's head hit a railing. A member of fans group Orsi Ribelli later said that only the father was hit.
In another violent incident in French football on Saturday, a Rodez player was attacked in a Ligue 2 match against Bordeaux, resulting in the game being abandoned. Four men were arrested and the French league (LFP) will meet on Monday to discuss the incident.