The court struck from the roll the case of Isaac Kwame Amuah, the husband of Mandela's daughter Makaziwe, ruling there was insufficient evidence against him.
The US had asked South Africa to extradite Amuah on six counts of committing sexual offences and one of failing to appear in court in connection with allegations that he raped a student while he was a lecturer at a community college in Hartford, Connecticut.
Amuah, a native of Ghana, was arrested in December after the US requested his extradition, and had been out of jail on 500,000-rand (69,000-dollar, 51,000-euro) bail.
His wife, Makaziwe, was born in 1954 and is the former president's fourth child with his first wife, Evelyn Mase.