Urbaniak started his music education during high school in Łódź, and continued from 1961 in Warsaw in the violin class of Tadeusz Wroński. Learning to play on the saxophone alone, he first played in a dixieland band, and later with Zbigniew Namysłowski and the "Jazz Rockers", with whom he performed during the Jazz Jamboree festical in 1961. After this, he was invited to play with Andrzej Trzaszkowski, and toured the USA in 1962 with his band "The Wreckers", playing at festivals and clubs in Newport, San Francisco, Chicago, Washington, and New York City.

After returning to Poland, he engaged on work with Krzysztof Komeda's quintet (1962-1964). Together, they left for Scandinavia, where, after finishing a couple of contracts, Urbaniak remained until 1969. There he created a band with Urszula Dudziak and Wojciech Karolak, which gained considerable success and was later to be the starting point for the famous "Michał Urbaniak Fusion".

After Urbaniak returned to Poland and the violin (which he abandoned for the saxopohone during the time in Scandinavia), he created the self-named "Michał Urbaniak Group", to which he invited, among others, Adam Makowicz (piano) and Urszula Dudziak (vocals). They recorded their first international album, Parathyphus B, and played on many festivals, including Jazz Jamboree in 1969-1972. During the Montreux'71 festival, Urbaniak was awarded by the prestigious Berklee College of Music in Boston. After many triumphant concerts in Europe and the USA, in May 1973 he played for the last time before a Polish audience and emigrated with Urszula Dudziak to the United States.

In spite of getting an award from Berklee, he did not study there. Recommended by John Hammond, Urbaniak signed a contract with Columbia Records, who published the west-German album Super Constellation under the name Fusion. For the promotion tour, he invited Polish musicians, including Czesław Bartkowski, Paweł Jarzębski, and Wojciech Karolak. In 1974, Urbaniak formed the band Fusion, and introduced melodic and rhythmic elements of Polish folk music into its music.

Urbaniak was now playing on a custom-made, five string violin furnished especially for him, on a violin synthesizer, and on a lyricon. His fusion with a hint of folklore was becoming popular among the leaders of American jazz, and also provided occasions for many new musicians (Harold Williams, Steve Jordan, Marcus Miller, Kenny Kirkland). He started to play in well known clubs such as Village Vanguard and Village Gate, in famous concert halls such as Carnegie Hall. In this period he played with such stars as Weather Report, Herbie Hancock, Chick Corea, George Benson, and Billy Cobham.