The incidents are believed to have taken place during the side's 4-0 win over Paris Saint-Germain in the Universal Cup, currently taking place in Forte dei Marmi in Tuscany, on Sunday.
Players' agent Mino Raiola, who represents Mario Balotelli and Zlatan Ibrahimovic among other top stars, sounded the alarm when he posted a message about the scenes on Twitter late on Sunday.
"In shock about today's Milan/PSG in Universal Cup, parents booing colour ten year olds. Heads up boys we're stronger than weak ignorant racists," said Raiola.
Milan on Monday did not confirm whether the incidents took place, but said if confirmed they were "unacceptable".
"We have been told of alleged incidents of a racist nature during yesterday's game between Milan and PSG in which coloured kids were targeted by 'people' attending the game," read the statement.
"We do not want to amplify or exaggerate anything, but we sincerely hope the allegations are unfounded or that it has been an isolated case.
"However, if they are true, it is absolutely unacceptable."
AC Milan's team went on to win the tournament, beating Inter Milan 4-0 in the final.
A club statement said: "Milan thoroughly deserved to win the tournament in what has been a big footballing and life experience, a group that has been strengthened after Sunday's alleged racist incident and now nothing but satisfaction for their success out on the pitch."
It is the latest in a long line of incidents of a racist nature to sully Italian football.
In January 2013, former Milan forward Kevin Prince-Boateng reopened the debate into how to tackle racism in football when he and several other black players were targeted by racists during a friendly with a lower division side.
Boateng walked off the pitch, his teammates followed and the game, against Pro Patria, was abandoned.
Boateng and former teammate Balotelli were targeted by monkey chants later that season by fans of rival Serie A side Roma.
More recently, former Italy and AC Milan coach Arrigo Sacchi kicked up a storm that warranted a stiff response from the Italian government when he complained under-20 teams in Italy contained "too many blacks".
Graziano Delrio, the State Secretary to Prime Minister Matteo Renzi who also holds responsibility for sport in the Italian council of ministers, hit out: "The Italy of 30 years ago is not the Italy of today.
"Today there are young players who are Italian citizens in fact and by right given that they were born and raised in Italy, even if their parents had overseas roots.
"They are part of the young generations who go to our schools, who play on our football and sports fields.
"And the theme of skin colour is certainly not where we should start trying to revitalize our youth system."