The principal of Saint Ignatius College in the northern Sydney suburb of Riverview has informed former and current pupils of the allegations.
Paul Hine said in his letter that the allegations concerned "child sexual abuse over 30 years ago".
The Roman Catholic college is among the country's top private schools.
Mr Hine said the college was assisting New South Wales police with the complaint, which was made to the standards office of the Australian Province of the Society of Jesuits, the owners of the school.
In a statement, Mr Hine said: "The College and the Jesuits wish to express, in the strongest possible terms, their abhorrence of sexual misconduct or any form of abuse involving children.
"We wish to respond to past abuse and suffering with a commitment to healing, openness and accountability."
Mr Hine also encouraged any person who "believed they were harmed" while in the care of the school to get in touch.
As well as Mr Abbott, the school was attended by Barnaby Joyce, the minister for agriculture, and Anthony Fisher, who is archbishop of Sydney.
In 1997, Peter Bohrsmann, a 57-year-old teacher at the school, took his own life on school grounds after he was accused of sexual abuse. Bohrsmann had denied the allegations.
Australia's Royal Commission is currently investigating allegations of child sexual abuse at a variety of institutions including schools, churches, and orphanages.
The Commission's inquiry was launched by former Prime Minister Julia Gillard in 2013.
Police in Australia have received allegations of sexual abuse at a school attended by Australian Prime Minister Tony Abbott.