Born in East Berlin, Erpenbeck is the daughter of the physicist, philosopher and writer John Erpenbeck and the Arabic translator Doris Kilias. Her grandparents are the authors Fritz Erpenbeck and Hedda Zinner. In Berlin she attended an Advanced High School, where she graduated in 1985. She then completed a two-year apprenticeship as a bookbinder before working at several theaters as props and wardrobe supervisor.
