Suk was born in Křečovice. He studied at Prague Conservatory from 1885 to 1892, where he was a pupil of Antonín Dvořák and Antonín Bennewitz. In 1898, he married Dvořák's eldest daughter, Otilie Dvořáková (1878–1905), affectionately known as Otilka. He formed the Czech Quartet with three of his fellow students — Suk played second violin with them for most of his life. From 1922 he taught at the Prague Conservatory where his pupils included Bohuslav Martinů and Rudolf Firkušný. He died in Benešov.
Suk's early works show the influence of Dvořák and Johannes Brahms, while later pieces use more extended harmonies to create a more personal and complex style. Unlike many of his countrymen, he made little use of Czech folk music. His best known works are probably the youthful Serenade for Strings (1892) and the Asrael symphony in C minor, (1906), a work written in response to the deaths, firstly, of his father-in-law, and later, his own wife. Norman Lebrecht has singled out Václav Talich's 1952 recording of the Asrael Symphony with the Czech Philharmonic Orchestra on Supraphon as #19 in his list of the 100 best recordings of the century.
Other pieces include the Fairy Tale Suite (1900), the cycle of piano works Things Lived and Dreamed (1909), and the trilogy of symphonic poems A Summer's Tale (1909), The Ripening (1917) and Epilogue (1929, for soprano, baritone and bass soli, chorus and orchestra).
Suk was the grandfather of the violinist Josef Suk.