A violin student from age five, Oistrakh graduated from the Odessa Conservatory in 1926 and made his Moscow debut in 1929. He gave recitals throughout the Soviet Union and eastern Europe and in 1937 won first prize in the Eugène Ysaÿe violin competition. From 1934 he taught violin at the Moscow Conservatory.

Oistrakh was first heard in western Europe and the United States through his recordings of 20th-century Russian works as well as the classical violin repertory. From 1951 he toured extensively in Europe and from 1955 in the United States.