Gordimer, who won the literature prize in 1991, three years before the end of white minority rule, died peacefully in her sleep at her home in Johannesburg on Sunday, the family said in a statement. Her son Hugo and daughter Oriane were with her at the time, it said.
Gordimer wrote 15 novels as well as several volumes of short stories, non-fiction and other works, and was published in 40 languages around the world, according to the family statement, which was released by a law firm.
"She cared most deeply about South Africa, its culture, its people, and its ongoing struggle to realise its new democracy," the family said.
They said her "proudest days" included winning the Nobel Prize and giving evidence in the 1980s on behalf of a group of anti-apartheid activists who had been accused of treason.
Gordimer was first a fiction writer. As a white South African who hated apartheid's dehumanisation of blacks, she also played a political role in her country's troubled history.
During the apartheid years, she praised Nelson Mandela, the prisoner who later became president, and accepted the decision of the main anti-apartheid movement, African National Congress, to use violence against South Africa's white-led government.
"Having lived here for 65 years," she said, "I am well aware for how long black people refrained from violence. We white people are responsible for it."
Gordimer said her first "adult story", published in a literary magazine when she was 15, grew out of her reaction as a young child to watching the casual humiliation of blacks. She recalled blacks at the shops of the mining town near Johannesburg where she grew up being barred from touching clothes before buying, and police searching the maid's quarters at the Gordimer home for alcohol, which blacks were not allowed to possess.
That "began to make me think about the way we lived, and why we lived like that, and who were we", she said in a 2006 interview for the Nobel organisation.
She said she resisted autobiography, asserting that journalistic research played no part in her creative process.
Telling Times, a 2010 collection of her non-fiction writing dating to 1950, offers some glimpses of her own experience. She wrote in a 1963 essay of a meeting with a poet giving her an idea of a life beyond her small home town and her then aimless existence.
Gordimer's first novel, The Lying Days, appeared in 1953, and she acknowledged that it had autobiographical elements. A New York Times reviewer compared it to Alan Paton's Cry The Beloved Country, saying Gordimer's work "is the longer, the richer, intellectually the more exciting".
She won the Booker Prize in 1974 for The Conservationist, a novel about a white South African who loses everything.
Among Gordimer's best-known novels is Burger's Daughter, which appeared in 1979, three years after the Soweto student uprising brought the brutality of apartheid to the world's attention.
Some readers believe the family at its centre is that of Bram Fischer, a lawyer who broke with his conservative Afrikaner roots to embrace socialism and fight apartheid. The story is salted with real events and names - including Fischer's. The main character is a young woman on the periphery of a famous family who must come to terms with her legacy and her homeland.
"Gordimer writes with intense immediacy about the extremely complicated personal and social relationships in her environment," the Nobel committee said on awarding the literature prize in 1991.
In her Nobel acceptance speech, Gordimer said that as a young artist, she agonised that she was cut off from "the world of ideas" by the isolation of apartheid. But she came to understand "that what we had to do to find the world was to enter our own world fully, first. We had to enter through the tragedy of our own particular place".
After the first all-race election in 1994, Gordimer wrote about the efforts of South Africa's new democracy to grapple with its racist legacy. She remained politically engaged, praising South Africa for the progress it had made, but pushing it to fulfil its hopes.
A private memorial service is expected to be announced at a later date.