Jiří Kodet came from a long-established Czech theatrical family, the Steimar family, and an artistic family, the Kodet family. His parents were Czech actress Jiřina Steimar and sculptor Jan Kodet. Following his parents' divorce, his mother remarried Jaroslav Juhan, a car racer, but he eventually emigrated, which had a significant impact on Jiří Kodet's educational path. He was expelled from grammar school and was initially not accepted into the Academy of Performing Arts in Prague (DAMU) until he was accepted on his second attempt.
Jiří Kodet began his theatre career at the East Bohemian Theatre in Pardubice, where he worked from 1961 to 1962. He then joined the Artistic Military Ensemble, based in Pohořelec, Prague, in 1962, and toured extensively throughout former Czechoslovakia. His future colleagues from the Drama Club, including Jiří Hrzán, Jiří Zahajský, and Petr Skoumal, were also part of the ensemble.
He was later sought out by Jan Kačer, who was assembling a troupe for the Petr Bezruč Theatre in Ostrava, and Kodet worked there from 1963 to 1965. From 1966, he played at the Prague Drama Club, where some members of the Ostrava ensemble had also moved. In 1991, he became a member of the drama company of the National Theatre in Prague.
Throughout his lifetime, Jiří Kodet played numerous small and episodic roles in film and television, but it was not until later in his life that he was able to take on more significant roles, primarily thanks to director Jan Hřebejk, who cast him in his films Divided We Fall and Cosy Dens, the latter of which was his most successful film to date.