"The show provides a first look into a high-profile South African family," the producers said in a statement.
The stars of the show, Zaziwe Dlamini-Manaway, 34, Swati Dlamini, 32 and Dorothy Adjoa Amuah, 27, promise to "showcase contemporary independent women in South Africa", it said.
"Their aim is to showcase the new Africa and give viewers a peek into its level of sophistication and its exciting potential," said the statement.
It will trace the daily lives of the American-schooled women who lead glitzy lives among Johannesburg's rich and famous, it said.
"These girls may have grown up abroad but they have all chosen to come back home to South Africa and bring the best that they have gathered in their international experiences and studies," it said.
"They feel that they can make a positive contribution to the continent," said the statement.
Mandela's daughter Zenani, born with his second wife Winnie Madikizela-Mandela, is the mother of the two Dlamini women. Amuah is the step-daughter of Makaziwe Mandela, one of Mandela's children with his first wife Evelyn.
The producers did not say what the rest of Mandela's family thinks of the show, but said "they believe they have fought for the right for their children to choose their own destiny and their own path".
The show would be the latest commercial initiative connected to Mandela. Two months ago, a local clothing company launched a fashion line to raise money for Mandela's AIDS charity.
The clothes were last week paraded at a Fashion Week.
It is not clear whether the ailing Nelson Mandela, now 93 and living in his village home, will feature in the show.