Abbasi came with his parents to the United States and grew up in Los Angeles. Jim Hall, Pat Metheny, and Bill Frisell were successively his musical influences. He studied at the University of Southern California and Manhattan School of Music jazz and classical music, then he went to India, where he learned from percussionist Alla Rakha.
1987 he moved to New York City, where he has since worked. In 1991 he released his first album, which included the talent of Bob Mintzer, Kenny Werner, Gary Thomas, Peter Erskine, Marc Copland, and Michael Formanek. Since then he has played in the fusion genre, post-bop, hard bop, and jazz standards. Since the mid-1990s, Abbasi has operated as a music teacher and composer. In addition, he has worked as musical director and producer for singer Kiran Ahluwalia on his album Wanderlust (2008).
On his 2005 album Incurred Snake Charmer, which included Indian vocalist Kiran Ahluwalia, Abbasi combined jazz and Indian music in his compositions. He is currently working with his Rez Abbasi's Acoustic Quartet (RAAQ), which includes vibraphonist Bill Ware, bassist Stephan Crump, and drummer Eric McPherson. With Vijay Iyer, Rudresh Mahanthappa, Kiran Ahluwalia, John Weidenmüller, and Dan Weiss he recorded the album Things to Come, for Sunnyside Records. This album was chosen by Down Beat magazine as one of the best albums of the decade. In addition, Abbasi was awarded the Chamber Music America Grant.