Müller was the son of the noted German poet Wilhelm Müller. Originally a student of Sanskrit, Müller turned to comparative language studies, and around 1845 he began studying the Avesta, the Zoroastrian sacred scripture written in Old Iranian. This interest led him to the study of comparative religion and to the editing of the most ancient of Hindu sacred hymns, the Rigveda, which was published after he had settled at the University of Oxford (184975). There he was appointed deputy professor of modern languages (1850) and professor of comparative philology (1868). While at Oxford he sought to popularize comparative studies of Indo-European language.

Müller's essays on mythology are among his most appealing writings. His exploration of mythology also led him further into comparative religion and to the publication of The Sacred Books of the East, begun in 1875. Of the 51 volumes, including indexes, of translations of major Oriental, non-Christian scriptures, all but three appeared under his superintendence during his lifetime. In his later years, Müller also wrote on Indian philosophy and encouraged the search for Oriental manuscripts and inscriptions. Among such discoveries were early Indian Buddhist scriptures written in Japan.