Peierls's father, Heinrich Peierls, was the managing director of the extensive cable factory of the Allgemeine Elektrizitäts-Gesellschaft (AEG) in the Berlin suburb of Oberschöneweide. In 1898 he married Elisabeth (Elly) Weigert, his cousin. Peierls was the youngest of three children. Elly Peierls died in 1921, when Peierls was fourteen, and his father shortly afterwards married Else; they remained in Berlin until 1939 when they left Germany and, after a brief stay in Britain, settled in New York where Heinrich Peierls died in 1945.

Family letters and cards were sent to Peierls often with great frequency by his father and stepmother Else, from their Berlin home or from various holiday addresses. None of Peierls's letters have survived from the early years though it is clear that he was also an assiduous correspondent. Blank pages were often used by him for mathematical calculations.