The boy has been suspended after allegedly also hurling vile abuse at a teacher while playing for Stewart’s Melville College last Saturday.
Shocked parents are understood to have watched from the sidelines as the boy used a deeply offensive term against a black opponent.
A spokeswoman for the £11,600-a-year school said: “A pupil at Stewart’s Melville College has been suspended for gross verbal abuse of a member of staff. A further allegation of racial abuse by the same pupil has subsequently been reported to the police and is currently under investigation.
“At ESMS we promote a culture of respect and tolerance and take such matters very seriously.”
The second-year pupil allegedly launched his foul-mouthed tirade during the Stewart’s Melville game away to Aberdeen-based Robert Gordon’s College.
Fellow 12 to 14-year-olds are understood to have heard the alleged abuse of the teacher – thought to be the referee – and his opponent.
Aside from being suspended from school, the boy is understood to have been banned from representing the school at rugby.
One parent said: “Racism should not be tolerated at all, including on the rugby field.”
The Ravelston school has a strong sporting heritage and counts Scottish rugby greats Doddie Weir and Finlay Calder among its past students.
The school is a four-time winner of the Brewin Dolphin Scottish Schools Cup Under-18 rugby championships.
Its onsite Ravelston Sports Club opened in 2000 and features extensive facilities for a range of sports.
The 750-student independent school offers day and boarding places for boys aged from 12 to 18.
Founded more than 150 years ago, its nine school values are kindness, respect, commitment, enthusiasm, responsibility, grace, appreciation, confidence and integrity.
The school also proudly displays its sporting history and extols the virtues of athletic pursuits on its website.
“Former pupils have gone on to become professional sportsmen and women, Olympians, British Lions and international medal winners,” it reads.
“Their success is an inspiration to the boys and girls who are still in school and who regularly represent their country and city in sports such as rugby, hockey, golf, tennis and football.”
Inspector Murray King of Aberdeen police said: “We are aware of comments being made at a rugby match in Aberdeen on March 2nd and we are liaising with the schools involved.
“Our inquiries are ongoing in order to establish whether a crime has been committed.”