Brabham was found guilty of one count of rape and one count of indecent treatment of a girl under the age of 12. He was found not guilty of another five charges of indecent treatment. The offenses occurred between 2003 and 2007.
The judicial proceedings started in October 2013 after the victim told her mother of the abuse.
Brabham's career in motorsport saw him become the 1989 British Formula 3000 champion, one year after finishing runner-up in the British Formula 3 Series.
He stepped up to F1 with minnows Life in 1990 but failure to pre-qualify in the first two rounds of the season prompted Brabham’s early exit from the sport.
He claimed victory at the 1991 Sebring 12 Hours with brother Geoff and former F1 racer Derek Daly before making a couple of IndyCar appearances on the Gold Coast in 1993 and 1994, becoming the first Australian to do so. Brabham retired in 1995.
After the verdict, the court was told he had a criminal history. Brabham was kept in custody and is scheduled to be sentenced next month.