He was born in Odessa, Ukraine (then part of the Soviet Union) and is the son of Tamara Rotareva and violinist David Oistrakh. He attended the Central Music School in Moscow and made his concert debut in 1948. From 1949 to 1955 he studied at the Moscow Conservatory, winning first prizes and international competitions in Eastern Europe. He then joined the faculty of the Conservatory in 1958, becoming a lecturer in 1965. Since 1996 Igor Oistrakh has held the post of Professor of the Royal Conservatory in Brussels.
He has appeared frequently internationally, both as a soloist and in joint recitals with his father, or with his father conducting.
He is noted for his lean, modernist interpretations.