Daniil Shafran was born in Petrograd (later Leningrad, then Saint Petersburg) in 1923. Even from before his birth he was surrounded by music. His mother and father were music students when he was born. His father, Boris Shafran, went on to be principal cellist of the Leningrad Philharmonic Orchestra and his mother, Frida Moiseyevna, was a pianist. He recounted how, as his mother went into labour, his father was practicing passages from Haydn's D major Concerto in preparation for a recital, and was reluctant to go to the hospital until he had mastered a difficult technical passage.