Richard Lewis Abrams was born September 19, 1930, in Chicago, Illinois, the second of nine children of Milton and Edna Abrams. He attended DuSable High School, where classmates included future musicians Charles Davis, Richard Davis, John Gilmore, Johnny Griffin, Laurdine Patrick, and Julian Priester, though Abrams himself skipped the school's celebrated music program under Walter Dyett in favor of sports. In 1946 he left school to focus on music, beginning piano lessons with a classically trained church pianist before studying counterpoint, keyboard harmony, theory, and composition at Chicago's Metropolitan School of Music (later merged into Roosevelt University). He soon left formal study behind, teaching himself from books, including Joseph Schillinger's composition texts, while working a day job at a printing company and absorbing Art Tatum, Charlie Parker, Thelonious Monk, and especially Bud Powell from records.

Through the 1950s Abrams worked Chicago's blues, R&B, and hard-bop circuits, backing visiting leaders including Dexter Gordon, Max Roach, Ruth Brown, and Woody Shaw, and composing and arranging for pianist King Fleming. He co-founded the quintet MJT+3, recording Daddy-O Presents MJT+3 in 1957 with several of his own compositions. Around 1961 he organized a rehearsal big band, the Experimental Band, at Chicago's C&C Lounge, using it to test the Schillinger-influenced compositional ideas he was developing; the band drew in younger Chicago players, several of whom later credited Abrams directly with shaping their musical direction.

In May 1965 Abrams joined pianist Jodie Christian, composer Phil Cohran, and drummer Steve McCall to organize a new musicians' collective; at its second meeting Abrams was elected president, and by month's end the group had taken the name Association for the Advancement of Creative Musicians (AACM). Abrams led the AACM's composition classes when it opened a school in 1967 and served as the organization's first president. That same year he adopted the forename Muhal (a word he later said meant "number one," of unclear origin) and recorded his leader debut, Levels and Degrees of Light, for Chicago's Delmark Records; the album gave saxophonist Anthony Braxton, violinist Leroy Jenkins, and bassist Leonard Jones their recording debuts, and set a direction that AACM contemporaries including Henry Threadgill and the Art Ensemble of Chicago would follow.

Through the 1970s Abrams composed for symphony orchestras, string quartets, and big bands alongside a steady run of small-group leader dates, mostly for the Italian label Black Saint. He formed a sextet from AACM members in 1972 (with Threadgill, Wallace McMillan, Reggie Willis, Steve McCall, and Kalaparusha Difda) that played the Berlin Jazz Festival in 1973, followed by a solo concert at Montreux and a European tour with the Art Ensemble of Chicago in 1974. He recorded as a sideman during this period with Marion Brown (Sweet Earth Flying, 1974), reunited on record with Braxton for the duo album Duets 1976, and appeared on Roscoe Mitchell's Roscoe Mitchell Quartet (1976) alongside George Lewis. Abrams relocated to New York in 1976, moving his family the following year, and continued recording annually for Black Saint, including the sextet date 1-OQA+19 (1978) with Braxton and Threadgill and the duo album Sightsong (1976) with Art Ensemble bassist Malachi Favors. He also served on National Endowment for the Arts jazz peer-review panels in the late 1970s and helped establish the AACM's New York chapter, which began presenting concerts there in 1982.

The 1980s and 1990s brought Abrams's largest-scale work: three albums by the Muhal Richard Abrams Orchestra (Rejoicing with the Light, 1983; The Hearinga Suite, 1989; Blu Blu Blu, 1991) and one by his octet (View from Within, 1985), all on Black Saint, alongside duo recordings with pianist Amina Claudine Myers, violinist Leroy Jenkins, bassist Cecil McBee, and saxophonist Roscoe Mitchell. In 1990 he became the first recipient of the Jazzpar Prize, and in 1997 he received a Foundation for Contemporary Arts grant. His classical-side work included a String Quartet No. 2, performed by the Kronos Quartet at Carnegie Recital Hall in 1985, and a 1989 album of his compositions recorded by Finland's UMO Jazz Orchestra with Abrams conducting and arranging.

Abrams remained active into his eighties, reuniting on record with George Lewis and Roscoe Mitchell for the trio album Streaming (2006) and recording solo piano dates The Visibility of Thought (2001) and Vision Towards Essence (2007), plus duo sets with Mitchell (Spectrum, 2009) and with Lewis and saxophonist Fred Anderson (SoundDance, 2011). In 2013 he joined Jack DeJohnette, Mitchell, Threadgill, and bassist Larry Gray for a Chicago Jazz Festival reunion concert, later released as Made in Chicago (ECM, 2015). He was named a United States Artists Prudential Fellow in 2008 and a National Endowment for the Arts Jazz Master in 2010, and received the Vision Festival's Lifetime Achievement Award later that year. Muhal Richard Abrams died at his home in Manhattan on October 29, 2017, at age 87.

Abrams was almost entirely self-taught, building a personal harmonic and compositional language out of Schillinger technique, close listening to Bud Powell and Art Ellington-and-Henderson-style big-band writing, and a restless curiosity that ranged from stride and ragtime through bebop into fully open improvisation, often within a single performance. As a bandleader he moved comfortably between a lone piano, small collaborative units, and the dense, through-composed voicings of his orchestra, treating instrumentation itself as compositional material (harp, accordion, and extended woodwind doublings turn up across his catalog). His deepest influence, though, ran through people rather than records: as the AACM's founding president and the leader of its Experimental Band, he was, by his own younger colleagues' account, a constant source of scores, reading lists, and encouragement for a generation that came to include Braxton, Threadgill, Roscoe Mitchell, and the members of the Art Ensemble of Chicago, several of whom made their recorded debuts on his own albums.