Shaw grew up in Newark, New Jersey, and began his study of music at the age of 11, later attending Newark Arts High School. Early in his career he was influenced by Clifford Brown, Lee Morgan, Fats Navarro, Booker Little, Dizzy Gillespie (with whom Woody Jr's father had gone to high school), Freddie Hubbard, amongst others, yet the influence of saxophonist Eric Dolphy, with whom he played and recorded in the 1960s, and John Coltrane, were equally as important to the development of his style and concept as a trumpeter and composer. He worked during the 1960s with such greats as Horace Silver, Max Roach, and Art Blakey. During this period he also recorded for Blue Note Records as a sideman with Andrew Hill, Jackie McLean, Chick Corea, McCoy Tyner, and others. Beginning in the mid-1970s he worked primarily as a leader.
Shaw had the misfortune of coming into his own as a band leader during the early 1970s, a time when interest in acoustic jazz was at a low ebb and even many of Shaw's idols were foresaking traditional jazz to explore jazz-rock fusion. Shaw saw himself as an heir to the musical tradition of great trumpeters such as Dizzy Gillespie, Fats Navarro, and Clifford Brown, and felt determined to uphold the highest artistic standards despite a relative lack of commercial success. He released several albums on the small Muse label, then in 1978 was signed to Columbia Records and recorded the albums Rosewood, Stepping Stones, Woody III, For Sure, and United. Rosewood was nominated for 2 Grammies and was voted Best Jazz Album of 1978 in the Down Beat Reader's Poll, which also voted Woody Shaw Best Jazz Trumpeter of the Year and #4 Jazz Musician of the Year.
Throughout the 1980s Shaw continued performing and recording as a leader with sidemen such as pianists Onaje Allan Gumbs, Mulgrew Miller, and Larry Willis, bassist David Williams, drummer Terri Lyne Carrington, and trombonist Steve Turre among others. During this time he also worked on projects with saxophonists Kenny Garrett and Dexter Gordon, as well as fellow trumpeter Freddie Hubbard. On 27 February 1989, Shaw was involved in an accident at the DeKalb subway station in Brooklyn, NY, in which his left arm was severed. The cause of the accident remains unclear, though Shaw had extremely poor eyesight, and allegedly had been suffering from medical and drug-related problems for many years.
On 10 May 1989, Shaw died from kidney failure.
As a musician and trumpeter, Shaw was held in remarkably high esteem by his colleagues. Miles Davis, a notoriously harsh critic of fellow musicians, once said of Shaw: "Now there's a great trumpet player. He can play different from all of them. Shaw is often credited with developing an improvisational approach based on larger intervals, like fourths and fifths, instead of the smaller intervals more easily playable on the trumpet.