Oistrakh studied with his father, the famous violinist David Oistrakh, and also attended the Central Music School in Moscow, making his concert debut in 1948. He then studied at the Moscow Conservatory (1949-55), winning first prizes, while still a student, at international competitions in Budapest, Hung., and Poznan, Pol. He joined the faculty of the Moscow Conservatory in 1958, initially assisting his father and later, in 1965, becoming a lecturer.
Oistrakh performed abroad frequently in Europe and America, occasionally performing in joint recitals with his father or performing as a soloist with his father as conductor.