News agency dpa said on Sunday the writer had died on Friday after a "short, serious illness," quoting her nephew Walter Zweig.
She was born in 1932 in Leobschütz, now part of southern Poland.
Her family fled the Nazis in 1938 and headed to Kenya. She recounted her childhood there in "Nowhere in Africa".
Zweig returned to Germany in 1947 and started a career as a writer.
Her most successful book was "Nowhere in Africa," published in 1995, and a movie adaptation of it won an Oscar for Best Foreign Language Film in 2003.