Turetzky was born and raised in Norwich, Connecticut. He received a master's degree in music history from the University of Hartford. In his youth, he was drawn to classical jazz music, playing professionally in that style at his first performances. His aspiration to be a jazz player was encouraged by many of the older swing stars. Turetzky continues to play classic jazz, and appears regularly at jazz festivals. He also plays the guitar, piano, and banjo.

Turetzky first recorded in 1964, featuring the work of American composers George Perle, Edgard Varèse, Kenneth Gaburo, Donald Martini, Ben Johnson, and an early instrument and tape piece by Charles Whittenburg. Recording activities continued with records on labels Nonesuch, Son Nova, Are Antigua and Desto. He has worked with Charles Mingus, and has made a series of recordings on the Nine Winds label with improvisational musicians George E. Lewis, Vinny Golia, Waded Leo Smith, Mike Wofford, and others.

Turetzky is a Distinguished Emeritus Professor of Music at the University of California, San Diego. His former students include bass virtuosos Mark Dresser - who now holds Turetzky’s former UCSD faculty position - Karl E. Siegfried, and Nathan East. Turetzky is married to flutist Nancy Turetzky, they have two sons and a daughter, and live in Del Mar, California.

Turetzky has performed and recorded more than 300 pieces written by and for him. He is a composer whose music has achieved some prominence, as have his interpretations of early music and composers like Domenico Dragonetti. Turetzky has appeared as a featured soloist in the major music centers of the world and is the most widely recorded solo doublebass player. Turetzky is a versatile musician, conversant in chamber, baroque, improvisational, classical, jazz, renaissance music, and many different genres of world music. He has also developed a special affinity for klezmer music.

In addition to The Contemporary Contrabass, Turetzky has co-edited a book series called The New Instrumentation; seven of a planned eight volumes have been finished. Turetzky wrote an introduction to The Autobiography of Pops Foster: New Orleans Jazz Man which spoke to the early development of jazz bass playing.

Bernard Jacobson of theChicago Daily News described Turetzky as "a virtuoso of caliber unsurpassed by any other practitioner of his instrument today."