Born in London as the third of four children, Hennessey, who came from a musical family, began learning piano at the age of six. After his military service, he began working as a journalist. He has written for many jazz magazines in Europe and North America and worked for 27 years as a correspondent and international editor for the US magazine Billboard, before retiring in 1994. He specialised in international copyright and intellectual property, and advocated strengthening of copyright protection for the music industry. He also co-founded international industry magazines such as Music Week and Music & Media, and wrote books on the music business and biographies of jazz musicians Kenny Clarke and Johnny Griffin. As a pianist he was a member of Chas Burchell's band, with which he recorded two albums. He also joined the Paris Reunion band with Nat Adderley, toured with Adderley, Billy Mitchell, Arthur Blythe, Benny Golson, Keter Betts, Jimmy Cobb, and Jan Harrington, and worked as an accompanist for Buddy DeFranco, Nathan Davis, Johnny Griffin, Duško Gojković, and Ronnie Scott.
- Rogers, Eddie; Hennessey, Mike (1964). Tin Pan Alley. London: Robert Hale.
- Scott, Ronnie; Hennessey, Mike (1979). Some of My Best Friends Are Blues. London: W. H. Allen. ISBN 0491022395.
- Hennessey, Mike (1990). Klook: The Story of Kenny Clarke. London: Quartet Books. ISBN 0704325292.
- The Little Giant : the Story of Johnny Griffin. London: Northway Publications. 2008. ISBN 9780955090851.
- Shades of Chas Burchell (In+Out, 1993)
- Unsung Hero: The Undiscovered Genius of Chas Burchell (In+Out, 1995)
- Brazier, Lawrence (October 2003). "A Portrait of Mike Hennessey". Jazz Now. Retrieved 23 September 2018.
- Spahr, Wolfgang (23 August 2017). "Mike Hennessey, Trailblazing Billboard Editor and Jazz Booster, Dead at 89". Billboard. Retrieved 23 September 2018.
- "Berühmter Musikautor feiert in Durchhausen Geburtstag". Schwäbische (in German). 20 February 2008. Retrieved 23 September 2018.