The Nelson Mandela Foundation said in a statement that the car in which the girl, who had turned 13 two days ago, was travelling was the only vehicle involved in the accident.
The family has asked for privacy as they mourn this tragedy,' the statement added.
Friday is the first day of the World Cup, when South Africa take on Mexico here.
Mandela, 91, was feted by tens of thousands of spectators at the warm-up gig in Soweto's Orlando Stadium, where Archbishop Desmond Tutu introduced a slide-show of photographs about the anti-apartheid icon in between acts.
Mandela, who is expected to attend part of the opening game in Soccer City later, has eight other great-grandchildren
