Members of the Mandela family were in the cramped courtroom where Mbuso Mandela, 24, appeared. He has been in police custody since his arrest on Saturday.
According to South African law, due to the seriousness of the charge, his defense attorneys will have to present evidence to support his release on bail.
The rape allegedly took place in a toilet at a restaurant in Greenside, a Johannesburg suburb, on Aug. 7, police said.
Earlier this week, the teenager's family accused Winnie Madikizela-Mandela of trying to derail the complaint, a family spokesman said. Madikizela-Mandela, the late Mandela's divorced wife, sent her bodyguard to the 15-year-old girl's home, where he posed as a police officer, the spokesman said.
Madikizela-Mandela also met with the family, where she promised to ask the provincial police commissioner to handle the case and said her family would also hold a press conference, the spokesman said.
The teenager's family reported the rape when they did not hear from Madikizela-Mandela again.
Madikizela-Mandela's office has not responded to questions about the alleged interference.