He was born in Odessa, Russia, and studied violin as a child with Stoliarsky in Odessa, making his debut there at the age of 6. He then continued his studies with Stoliarsky at the Odessa Conservatory (1923-26) and appeared as soloist in Glazunov's Violin Concerto under the composer's direction in Kiev in 1927.
His recordings and performances of Shostakovich's concerti are particularly well known, but he was also a performer of classical concerti. He worked with orchestras in Russia, and also with musicians in Europe and the United States. Another famous recording is the one he made of Beethoven's Triple Concerto with Sviatoslav Richter and Mstislav Rostropovich. Both Shostakovich's and Aram Khachaturian's violin concerto are dedicated to him.
Oistrakh received his first and only training from the violin pedagogue Pyotyr Stolyarsky. Contrary to popular belief, Oistrakh was not a born virtuoso. He actually started by playing viola in the Conservatoire orchestra. Only a couple of months later he rose to the level of soloist and made his debut playing the Bach A minor concerto with the orchestra. A year later, he made his debut as a solo recitalist. He toured Russia for the next two years, and finally made his Leningrad debut on the Tchaikovsky violin concerto.
In 1936 Oistrakh won second prize at the Wieniawski Competition, losing to the 15 year old Ginette Neveu. This further dispels the myth that Oistrakh was a born virtuoso. He finally made a mark on the international scene by capturing top prize in the Queen Elisabeth Competition (then known as the Ysa˙e Competition) in Brussels. Oistrakh's career was set from this point, except for one small hitch - the Soviet Union was ultra-protective of its people and refused to let him leave. He continued to teach in the Moscow Conservatory, but when Russia went to war against Hitler, he went to the front lines and played for the troops to keep morale up.
For around ten years, Oistrakh played the 1702 Conte di Fontana Stradivarius that he traded for the 1715 Ex Marsick Stradivarius in June 1966. He was a well respected pedagogue, who spent his formidable years on the faculty of the Moscow Conservatory among such greats as Yuri Yankelevich and Boris Goldstein.
David Oistrakh was the father of violinist Igor Oistrakh. The two made numerous recordings together.
He passed away while in Amsterdam in 1974. His remains were returned to Moscow where he was interred in Novodevichy Cemetery.