Born in the Moravian town of Napajedla, Firkušný started his musical studies with the composers Leoš Janáček and Josef Suk, and the pianist Vilém Kurz.

Firkušný was also a devoted chamber player, and among his most prominent partners were cellists Pierre Fournier, Gregor Piatigorsky, János Starker, and Lynn Harrell; violinists Nathan Milstein and Erika Morini; violist William Primrose; and the Juilliard String Quartet.

He also gave many first performances of contemporary composers, not only Czech such as by his friends Martinů and Vítězslava Kaprálová but also Howard Hanson, Gian Carlo Menotti, Samuel Barber, and Alberto Ginastera.

Among his students were Yefim Bronfman, Eduardus Halim, Alan Weiss, Sara Davis Buechner, Carlisle Floyd, Kathryn Selby, Avner Arad, June de Toth, Richard Cionco, Robin McCabe, Anya Laurence, Natasa Veljkovic and Carlo Grante.

Firkušný retained his remarkable talents well into his later years and, for example, played a full Dvořák-Janáček-Brahms-Beethoven sonata recital in Prague on 18 May 1992 together with the violinist Josef Suk (the namesake and grandson of his teacher, and great-grandson of Dvořák).

[5][6] In 2007, his ashes and those of his wife, Tatiana Nevolová Firkušný, were reburied together in an honorary place at the Central Cemetery in Brno, close to his first teacher, Janáček, and directly next to the grave of Czech composer Jan Novák.

In 2012, coinciding with the 100th anniversary of his birth, there was a large festival held by Brno's Janáček Academy of Music and Performing Arts to commemorate the centennial, featuring many of his former alumni from the Juilliard School.