Zindzi Mandela is the youngest daughter of Nelson Mandela and anti-apartheid activist Winnie Madikizela-Mandela.
According to public broadcaster SABC, Zindzi Mandela died in a Johannesburg hospital in the early hours of Monday.
The cause of her death is yet to be made public.
Until her death, she was South Africa’s ambassador to Denmark.
Zindzi Mandela was Nelson Mandela's sixth child and his second with Winnie Madikizela-Mandela, his second wife.
The ANC spokesman Pule Mabe said her death was unexpected.
"This is untimely. She still had a role to play in the transformation of our own society and a bigger role to play even in the African National Congress (ANC)."
Minister of International Relations Naledi Pandor said: "Zindzi will not only be remembered as a daughter of our struggle heroes but as a struggle heroine in her own right."
Zindzi Mandela grew up during the anti-apartheid struggle. She endured years of struggle and harassment when her father was imprisoned on Robben Island along with her sister Zenani, and her mother Winnie.
It was Zindzi Mandela who read out Nelson Mandela's rejection of then-president PW Botha's offer for conditional release from prison at a public meeting in February 1985.
In recent times, she is mostly known for her vocal support for radical land reform in South Africa.
After her death, it means that only two of Nelson Mandela's six children are still alive: Zenani Dlamini, Zindzi's sister; and Pumla Makaziwe Mandela, a daughter from his first marriage, to Evelyn Mase.