She passed away on Monday evening surrounded by friends and family, a spokesperson said.
In recent years, Ms Mandela had become well known for detailing her cancer treatment. She was also open about her history of drug addiction.
The Nelson Mandela Foundation said her work was inspirational.
It said that she raised “awareness about cancer prevention” as well as “breaking down the stigma surrounding the disease”.
Ms Mandela also spoke candidly about her struggles with depression and the fact that she had been sexually abused as a child.
In addition, she campaigned for better road safety after her 13-year-old daughter was killed in a car accident in 2010. She later lost a son who was born prematurely. She is survived by four children.
Ms Mandela, who was the granddaughter of Nelson Mandela’s second wife, Winnie, documented her story in her autobiography When Hope Whispers.
Diagnosed with breast cancer at age of 32, she received treatment and was in remission but the illness later returned.
Last year, she confirmed that she had cancer in her liver and lungs, it then spread to other organs. She was being treated as an outpatient but was admitted to hospital just over a week ago.
“What do I tell my children? How do I tell them that this time around I may not get to live my life as a survivor? How do I tell them everything will be OK when it’s not? I’m dying… I don’t want to die,” she posted on Instagram early last month.
In an interview with Kaya FM in April, Ms Mandela said: “I’m learning to be okay with my eventuality.”
She was only 10 when her grandfather was released from prison in 1990 after 27 years in detention.
Ms Mandela had only ever known him as an incarcerated man, so when he was released she was just excited he was coming home.
Mr Mandela died in 2013 at the age of 95.
Source: bbc.com