German news agency dpa on Sunday cited her nephew Walter Zweig as saying the author died Friday after a "short, serious illness."
Zweig was born in 1932 in Leobschuetz, now part of Poland. In 1938, her family fled the Nazi persecution of Jews and moved to Kenya, where she attended a British school.
Zweig returned to Germany in 1947 and worked as a journalist for many years before she began writing novels.
Of her more than two dozen books "Nowhere in Africa," first published in 1995, was the most successful, retelling the story of her family's time in Kenya.
A movie adaptation won an Oscar for Best Foreign Language Film in 2003.