The death of Collins Chabane, minister in charge of public service and administration, is a big loss to the government and the country, President Jacob Zuma said in a statement.
The main opposition party, the Democratic Alliance, noted in a condolence message that two police officers who were acting as Chabane's bodyguards also died in the crash.
Chabane's car hit a truck that was making a U-turn on a highway near Polokwane, the capital of South Africa's Limpopo province, South African media reported.
Chabane planned the funeral of Mandela, the anti-apartheid leader and former prisoner who became president in South Africa's first all-race elections, with "great dignity and efficiency," Zuma's office said.
The funeral ceremonies for Mandela included a stadium memorial attended by US President Barack Obama and dozens of other leaders from around the world.
Chabane was a veteran of the fight against apartheid, the system of white racist rule that ended with Mandela's election in 1994, according to the presidential office. He was also a long-serving member of the national executive committee of South Africa's ruling party, the African National Congress.