Zweig is best known for her autobiographical novel, Nirgendwo in Afrika (Nowhere in Africa, 1998), based on her early life in Kenya, which was filmed and won an Oscar in 2002 for "Best Foreign Film". Her family, being Jewish, fled Nazi Germany, for Africa. They went from an urban life in Breslau (now Wroc?aw) to a farm in Kenya in 1938 when she was five. She attended an English boarding school while there. In 1941, the family received a postcard from her grandmother saying "we are very excited, we are going to Poland tomorrow", which implied Auschwitz. Zweig has returned to Kenya twice since leaving in 1947 at the age of 15. She found the farm had been destroyed.

Her teenage years in Germany were recounted in the autobiographical novel Irgendwo in Deutschland (Somewhere in Germany). Her father was given work as a judge in post-World War II West Germany, partly because there was no need to "denazify" him.

Her first African novel was Ein Mund voll Erde (A Mouth Full of Earth) in 1980. It won several awards, and describes an infatuation with a K?k?y? boy.

She had a long career as an arts editor on a Frankfurt tabloid. In later life, she began writing children's literature and then began her novels . Although she is a best selling author in German, she is not well known in the English-speaking world, except for Nowhere in Africa.