Inter Milan goalscorer Mario "Barwuah" Balotelli was racially abused by some home fans during Saturday’s 1-1 draw at Juve.
Racial chanting is not uncommon in Serie A with the league usually handing out small fines to clubs.
However, the media revulsion at Balotelli’s treatment in such a high-profile game could lead to heavier sanctions against Juve with the Turin police also investigating the matter.
“In the name of Juventus and the great majority of our fans, I express a firm condemnation of the racist chants against Inter player Mario Balotelli,” Cobolli Gigli told Italy’s ANSA news service.
“Together we must try to create a sporting culture which centres on respect for an opponent and the fight against racism.”
A section of Juve fans sang “a black Italian does not exist” towards Balotelli on Saturday.
The 18-year-old, an Italy under-21 international, is of Ghanaian descent but was born in Palermo.