Milan Polák studied at the Conservatory in Brno (under Lubomír Bartoň), and in 1991 he finished his studies at the Janáček Academy of Music and Performing Arts in Brno (under Valter Vítek).
He was a member of the State Philharmonic Orchestra in Brno, and the orchestra of the National Theatre in Bratislava, and since 1992 he has been a principal clarinetist of the Prague Chamber Orchestra, and during this time he played with this orchestra at many concerts in the world, e.g., Carnegie Hall, New York, the Cité de la Musique à Paris, the Cologne Philharmonic, the Salzburg Mozarteum, the Vienna Musikverein, the Teatro Colón in Buenos Aires, the Santori Hall in Tokyo, the Tchaikovsky Moscow State Conservatory, as well as performing in China, Singapore, Hong Kong, Mexico and Australia.
As a member of the orchestra he cooperated with a number of artistic personalities with renowned names. The conductors include, for instance, Sir Charles Mackerras, Václav Neumann, Gerd Albrecht and Trevor Pinnock. The list of the soloists has among others Rudolf Buchbinder, Maxim Vengerov, Barbara Hendricks, Mischa Maisky, Beaux Arts Trio, Ivan Moravec or Alice Sara Ott.
As a member of Prague Chamber Orchestra he recorded for the companies Supraphon, Denon, BMG, Decca, Telarc and others.
As a soloist and chamber musician he performed at many concerts and international festivals in the Czech Republic and abroad – Poland, Germany, Slovak Republic, Austria, Belgium, France, Spain, Italy, Holland, Turkey, Australia and USA.
In 1995 he gave the European premiere of Concert for clarinet and orchestra composed by Robert Livingston Aldridge. For the Czech Radio he recorded the piece Clarinettino composed by Ondrej Kukal.
Regarding to chamber music, he has performed with numerous ensembles. With the Pražák quartet he recorded the CD Pierrot Lunaire and Suite, Op. 29 by Arnold Schönberg for label Harmonia Mundi and Leoš Janáček Concertino and Claude Debussy Prelude to the Afternoon of a Faun.
He is a member of the Prague Wind Trio and Janáček Ensemble.
Since 1994 he has been a member of the international orchestra Solistes Europeéns Luxembourg.
He was a lecturer at the international courses in Žirovnice and since 2018 he has been the teacher at the annual International Music Master Classes in Brno.
Currently, in addition to his concert activities, he works as a professor, teaching clarinet and the chamber music at the Janáček Academy of Music and Performing Arts in Brno and Prague Conservatory. His students play in many orchestras in the Czech Republic as well as in Europe: Ensemble intercontemporain Paris, Gustav Mahler Jugendorchester, EUYO, orchestral academy of Czech Philharmonic, Prague Radio Symphony Orchestra, National Theatre Prague, Brno Philharmonic, Slovak National Theatre, etc.
He participated in organizing the international competition Czech Clarinet Art and Leoš Janáček International Competition in Brno.