Paris St-Germain forward Neymar was the last of five red cards in Sunday's bad-tempered Ligue 1 match, sent off for hitting Gonzalez.
On Twitter, Neymar later accused Gonzalez of racism and PSG said they would "strongly support" the Brazilian.
"We are sure that Alvaro is not racist," said Villas-Boas.
"Marseille and PSG are here to help find the truth about this controversy. I am behind my player."
Neymar and team-mates Leandro Paredes and Layvin Kurzawa, plus Marseille pair Jordan Amavi and Dario Benedetto, were dismissed after trouble broke out in the final few minutes of the game, which PSG lost 1-0.