Michael Moore began playing bass at 15, and later worked with his guitarist father in Cincinnati clubs. He studied at the Cincinnati College Conservatory and played at the local Playboy Club with Cal Collins and Woody Evans.
Moore toured Africa and Eastern Europe on a State Department-sponsored junket with Woody Herman's band in 1966, and recorded with Herman in New York and Dusko Goykovich in Belgrade.
During the seventies, he played with Marian McPartland, Freddie Hubbard, Jim Hall and Benny Goodman, as well as quartets led by the duos of Ruby Braff and George Barnes, and Chet Baker and Lee Konitz. In the late seventies, Moore teamed with Gene Bertonicini, a partnership that would extend through the eighties and nineties. Their recordings can be heard on the OmniSound, Stash and Chiaroscuro labels. He has also recorded with Jake Hanna, Warren Vache, Herb Ellis, Zoot Sims, Kenny Barron, and Michael Urbaniak.
Moore appears on the 2004 Chesky release Hot Club of 52nd Street along with Bucky Pizzarelli, Johnny Frigo, and Howard Alden. The album is a tribute to legendary jazz guitarist Django Reinhardt.