Labeled a "child prodigy", Zukofsky made his public debut at the age of nine playing the first movement of Mozart’s violin concerto No. 3. Aged 13, he gave his debut recital in Carnegie Hall. He was reported to have gone "through a difficult program without turning a hair or moving a facial muscle" and described as a "deadpan bundle of talent". The New York Times reviewer praised his technique, but also said that he played with "little emotion".
Zukofsky specializes in contemporary music and has worked with, performed, and recorded the works of such 20th-century composers as Milton Babbitt, Arthur Berger, Easley Blackwood, Henry Brant, John Cage, Elliott Carter, George Crumb, Morton Feldman, Philip Glass, Peter Mennin, Krzysztof Penderecki, Walter Piston, Wallingford Riegger, Giacinto Scelsi, Artur Schnabel, Roger Sessions, Ralph Shapey, Harvey Sollberger, Stefan Wolpe, Charles Wuorinen, and Iannis Xenakis.
John Cage composed his Freeman Etudes - Books I and II (Etudes I-XVII, 1977–1980) for Zukofsky.
He has released 60 recordings on the Sony, Camerata, CRI, and CP2 labels.
He has also worked as a professor of violin.
Zukofsky is the copyright contact for his parents, Louis and Celia Zufoksky. He maintains tight control of his parents' archive. In 2009, Paul Zukofsky wrote an open letter telling graduate students and scholars that "In general, as a matter of principle, and for your own well-being, I urge you to not work on Louis Zukofsky, and prefer that you do not."  In the letter, Paul Zukofsky required that graduate students ask him for permission to quote from his father's works in their dissertations (an extremely unusual practice), and made it clear that he might withhold such permission. Quoting from e. e. cummings (presumably without permission), he indicated that he believed that scholars write chiefly from self-interest and that their claims that their scholarship would help enhance Louis Zukofsky's artistic legacy were offensive:
I can perhaps understand your misguided interest in literature, music, art, etc. I would be suspicious of your interest in Louis Zukofsky, but might eventually accept it. I can applaud your desire to obtain a job, any job, although why in your chosen so-called profession is quite beyond me; but one line you may not cross i.e. never never ever tell me that your work is to be valued by me because it promotes my father. Doing that will earn my life-long permanent enmity. Your self-interest(s) I may understand, perhaps even agree with; but beyond that, in the words of e.e.cummings quoting Olaf: “there is some s I will not eat”.
Paul Zukofsky wrote in the letter that his chief concern was to derive income from his possession of copyrights in his father's work, not to censor what might be said, but it might well be the case that the unusual difficulty and expense of writing about Louis Zukofsky will affect the poet's legacy.
He is also known for his involvement in the removal of Arnold Schoenberg's archive from the University of Southern California. As of 1998, this archive resides in the Arnold Schönberg Center in Vienna, Austria.
- Zukofsky, Paul (1976). "On Violin Harmonics." In Perspectives on Notation and Performance ed. Benjamin Boretz and Edward T. Cone (New York: Norton, 1976). Essays reprinted from issues of Perspectives of New Music. The Perspectives of New Music series. ISBN 0-393-02190-4. ISBN 978-0-393-02190-5. ISBN 0-393-00809-6. ISBN 978-0-393-00809-8.
The Library Congress shows Zukofsky has partaken in more than 50 recordings over the past four decades. The following list is a sample—and only his first-time recordings of composers appear here, for brevity:
- Music for a 20th-century violinist (anthology of three decades of American music, 1940-1950-1960) [undated]
- Roger Reynolds: Roger Reynolds collection 1964–present (1964)
- Charles Ives: Sonatas for violin and piano, volumes 1 and 2 (1965)
- Iannis Xenakis: Akrata ; Pithoprakta / Iannis Xanakis. Capriccio for violin & orchestra ; De natura sonoris / Krzysztof Penderecki (1968)
- Richard Hoffmann: String trio (1969)
- Michael Sahl: Mitzvah for the dead, for violin and tape (1969)
- Roger Sessions, Piano sonata no. 3 - Charles Wuorinen: Duo for violin and piano (1971)
- Paul Zukofsky: New music for chamber orchestra (1972)
- George Crumb: Black angels - Charles Jones: String quartet no. 6 (1972)
- Elliott Carter: Double concerto for harpsichord and piano with two chamber orchestras; Duo for violin and piano (1975)
- Paul Zukofsky: Library of Congress Music Division concert, 1975-10-31, 3:00 p.m. (1975)
- Paul Zukofsky: Library of Congress Music Division concert, 1976-02-27 (1976)
- John Cage: Cheap imitation (1977)
- Georg Philipp Telemann: Trio sonata in A minor no. 5 from Essercizii musici (1978)
- Paul Zukofsky: Library of Congress Music Division concert, 1979-05-10 (1979)
- Paul Zukofsky: Colonial Symphony Orchestra (1980)
- Morton Feldman: Spring of Chosroes - Artur Schnabel: Sonata for violin and piano (1981)
- Edward Steuermann: Dialogues (1981)
- Paul Zukofsky: New music from the University of Iowa (1983)
- Philip Glass: Photographer (1983)
- Dane Rudhyar: Five stanzas ; Epic poem (1983)
- Charles Wuorinen: Tuba concerto - Glenn Lieberman: Dialectic (1983)
- Joel Krosnick - Library of Congress Music Division concert, 1984-11-07 (1984)
- Artur Schnabel: Sonata for solo violin (1985)
- Paul Zukofsky: Sinfóniúhljómsveit íslands (Íslensk hljómsveitarkvert - Icelandic orchestral music (1986)
- William Schuman: In praise of Shahn - Aaron Copland: Connotations - Roger Sessions: Suite from The black maskers (1988)
- Tōru Takemitsu: Piano-distance (1988)
- Paul Zukofsky: Juilliard Orchestra (1990)
- Jón Leifs: Visions and images sound recording (1991)
- Jón Nordal: Portrait (1991)
- Paul Zukofsky: Min-On Contemporary Music Festival '83 (1993)
- Benjamin Boretz: Group variations II for computer - J. K. Randall: Lyric variations for violin and computer (1993)
- Paul Zukofsky: Sessions, Mennin, Blackwood (2002)
- Paul Zukofsky: Shapey, Riegger, Piston, Crumb, Sollberger, Berger (2002)
- Milton Babbitt: Septet but equal, Fourplay (2003)
- Johann Sebastian Bach: Three sonatas and three partitas (2005)
- Nicolò Paganini: 24 caprices (2005)
- Paul Zukofsky: Third Inter-American Music Festival [1965-05-10] (2007)
- Slonimsky, Nicolas (1978). "Zukofsky, Paul". Baker's Biographical dictionary of musicians. (6th ed.). New York: Schirmer Books. p. 1953. ISBN 0-02-870240-9.
- Peters, Margot (2011). Lorine Niedecker: A Poet's Life. University of Wisconsin Press. p. 113. "On February 23, 1953, nine-year-old Paul Zukofsky had made his public debut playing the first movement of Mozart's Violin Concerto No. 3 at a New Haven Symphony youth concert."
- Harold C. Schonberg (1 December 1956). "Violinist Presents Difficult Program With Technical Accuracy at Debut Here". The New York Times. p. 17 (Section Family/Style).
- "Paul Zukofsky". Classical Archives. Retrieved 7 October 2010.
- "V083: Impact: USC School of Journalism". Arnold Schoenberg Center. Retrieved 7 October 2010.
- "Paul Zukofsky". All Music. Retrieved 7 October 2010.
- "Recordings". Musical Observations. Retrieved 7 October 2010.
- Zukosfky, Paul (17 September 2009). "Copyright Notice by PZ". Z-site. Retrieved 8 September 2011.
- "Fair Use Poetry Booklet". Retrieved 2011-09-09.
- Miller, Judith (12 July 1996). "Schoenberg Archives to leave U.S.C.". New York Times. Retrieved 7 October 2010.
- "Schoenberg Archives". University of Southern California. Retrieved 7 October 2010.
- "Information". Arnold Schoenberg Center. Retrieved 7 October 2010.
- "Lawsuit - XComp". Burris & Schoenberg LLP. Retrieved 7 October 2010.
- All-Music biography
- Paul Zukofsky recordings
- Copyright Notice by Paul Zukofsky
- New York Times on Schoenberg Archive