Magistrate Tefo Myambo ruled in Isaac Amuah's favour at an extradition hearing on Friday in Johannesburg, saying he was convinced the accuser was alleging rape to try to get money.
Amuah, a former professor at Manchester Community Technical College, left Connecticut 12 years ago while facing the charges, which he denies.
Amuah is accused of sexually assaulting a 34-year-old student inside his Connecticut apartment in 1993.
He was given permission to travel to South Africa while the case was pending and never returned.
Amuah is married to Mandela's oldest daughter, Makaziwe.