Shipp was raised in Washington, DC and began playing piano at six years old. He was strongly attracted to jazz, but also played in rock music groups while in high school. Shipp attended the University of Delaware for one year, then the New England Conservatory of Music. Shipp has long been a member of saxophonist David S. Ware's quartet. He has recorded or performed with many musicians, including William Parker, DJ Spooky, Joe Morris, Daniel Carter, Roscoe Mitchell and Mat Maneri.