The Universal Cup is an annual youth tournament featuring 48 teams from around the world - including Chelsea, Juventus, Inter, Ajax and Benfica - and is currently taking place in Forte dei Marmi in Tuscany.
On Sunday, AC Milan's Under-10s played against their PSG equivalents for a place in the semi-finals but their black players were booed and heckled throughout the match by parents on the sidelines.
It is not known which team the racist parents were following.
The Rossoneri completed the game, which they won 4-0, but expressed their anger to organisers after the match. They also consoled their black players who had been abused.
AC Milan published a statement on their official website, saying: "It has been brought to our attention that, during yesterday’s match between Milan-PSG, there were alleged incidents of racism towards Milan’s black players from certain 'people' in the stands.
"We do not wish to magnify the issue, but truly hope that these reports aren’t true or that it was simply a sporadic incident. If they were to be confirmed, then it would be simply unacceptable."Football agent Mino Raiola condemned the abuse on his official twitter account, labelling the hecklers as "weak, ignorant racists."
The tournament's organisers, who have not responded to Goal's request for comment, posted an anti-racism video featuring Cristiano Ronaldo and Lionel Messi on their Facebook page on Monday morning.
In shock about today's Milan/PSG in Universal Cup parents booing colour 10 year olds. Heads up boys we'r stronger then weak ignorant racists— Mino Raiola (@MinoRaiola) April 5, 2015
It is not yet clear if action has been taken against the alleged racists and whether the police have been informed about the incident.