The small house, where Nelson Mandela lived with his first wife, Evelyn, and where he brought Winnie after their marriage in 1958, was given last year by the South African President to the Soweto Heritage Trust.
The President's former wife, who for two years has run a museum on the site, claims it was not his to give away, especially since the "navels" - umbilical cords - of her children are buried there. She claims that the trust and the President are conspiring against her.
Meanwhile, for five rand (50p), tourists and Soweto residents can see the house where President Mandela began his African National Congress career, and to which he returned after his release from jail in 1990.
The plaque by the door says "Winnie Mandela and Family Museum". The museum has 1,000 visitors a month and, at the back of the house, visitors may buy souvenirs, including soil from the property. Ms Madikizela-Mandela lives in a grander Soweto house some way away.
The trust, which controls several sites linked to the struggle against apartheid, claims the house is the property of "the people of the world". Sydney Phuti, chief executive of the trust, said: "The place is not meant for one person. It belongs to the people of South Africa and the world."
A spokesman for Ms Madikizela-Mandela said: "Winnie is the defendant. The trust has made a deal with the President to get her out."
In a country where for years black people could not legally own property - except in government-created "homelands" - this is not a clear-cut case. The trust says that when President Mandela handed over Vilakazi Street he had bought it from Soweto council. But Ms Madikizela-Mandela claims that the council sale, in 1997, was illegal. She says the council did not deal properly with her 1985 application to buy the property.