Born in Tel Aviv, Israel in 1941, Shmuel Ashkenasi attended the Musical Academy of Tel Aviv and gave his first public performance while still very young. He came to the United States on a scholarship to study with Efrem Zimbalist at the Curtis Institute. The international music community discovered Ashkenasi quickly, at Belgium's Queen Elizabeth Competition, at Washington's Meriwether Post Competition (first prize) and at the Moscow Tchaikovsky Competition in 1962.

He performed with American orchestras such as the Philadelphia Orchestra, Boston Symphony, Chicago Symphony, National Symphony, Los Angeles Philharmonic, Atlanta Symphony, Vienna Symphony, Royal Philharmonic, and the orchestras of Berlin, Hamburg, Munich, Zurich, Rotterdam, Geneva and Stockholm; Ashkenasi has been the choice of many of the world's most distinguished conductors, including Stokowski, Böhm, Kempe, Leinsdorf, Kubelik, Skrowaczewski and Ancerl. In addition, as first violinist of the famed Vermeer Quartet, he has gained a reputation as one of the world's outstanding chamber musicians. 4 recordings he was involved in were nominated for Grammy awards.

He currently teaches violin and Chamber Music at the Curtis Institute of Music in Philadelphia as well as Roosevelt University in Chicago.