Turnovský was born in Prague. His father was familiar with the conductor George Szell, who helped in the beginnings of Turnovský's career. During World War II, at the age of 16, Turnovský was imprisoned in German concentration camp, due to his partially Jewish origin. He studied conducting at the Prague Academy of Music as a pupil of Karel Ančerl. He won the first prize at the International Conductors Competition of 1958 in Besançon, France.
Turnovský was appointed chief conductor of the Radio Symphony Orchestra Plzeň (1963–66), the Sächsische Staatskapelle Dresden and Semperoper (1966–1968), the Norwegian National Opera (1975–80), the Opera in Bonn (1979–83), and the Prague Symphony Orchestra (1992–95). He was also permanent guest conductor of the Czech Philharmonic Orchestra (1960–1968).
After the entry of the Warsaw Pact nations into Czechoslovakia (Prague Spring), Turnovský emigrated to Austria and was granted Austrian citizenship. However, following the revolutions of 1989 he returned to Prague.
After Turnovský gained Austrian citizenship, he conducted many more symphony orchestras, including the New York Philharmonic, the Cleveland Orchestra, the Detroit Symphony Orchestra, the London Symphony Orchestra, the Bavarian Radio Symphony Orchestra, l'Orchestre de la Suisse Romande, the Vienna Symphony, the Bamberg Symphony, the Toronto Symphony Orchestra, the City of Birmingham Symphony Orchestra, the Royal Liverpool Philharmonic, the Tokyo Metropolitan Symphony Orchestra, and other orchestras.
- "Turnovsky". Baron & Weingartner Artists. Archived from the original on April 30, 2006. Retrieved 2006-09-05.
- Aryeh Oron (August 2005). "Martin Turnovský biography". Bach Cantatas Website. Retrieved 2006-09-05.
- Pilka, Jiří (October 2008). "Osudy s orchestrem a s operou". Harmonie (in Czech) (9): 6–7.