Educated in Wellington, Kennedy was a piano teacher and music librarian in her early years. She graduated with a Bachelor of Music in Composition from Victoria University of Wellington and taught at Trinity College London.
Since 1986, she has been a freelance scriptwriter. Anne Kennedy published her first novel in 1988, and has since published six novels and books of poetry. Her most recent novel, The Last Days of the National Costume was featured on the Listener's Top 100 Books of 2013, and on the Nielson 2013 Bestseller's list in New Zealand adult fiction.
In 2006, Kennedy was a visiting writer at University of Hawai'i at Mānoa. She was a professor there for several years. Currently, she teaches creative writing at Manukau Institute of Technology. She is currently co-editor of literary journal Ika, and was co-editor of the online literary journal Trout.  and co-edited the 2005 Best New Zealand Poems series.
Her work has appeared in Landfall, Sport, NZ Listener, Southerly (Australia), and JAAM, and she has co-edited several other works including the 2005 Best New Zealand Poems series.
- 1985 Bank of New Zealand Katherine Mansfield Short Story Award.
- 1995 University of Auckland Literary Fellow
- 2004 Montana New Zealand Book Award for Poetry
- 2013 New Zealand Post Book Awards - Poetry category winner
- 2014 Fellowship for University of Auckland Residency at the Michael King Writers' Centre
- 2014 Nigel Cox Unity Books Award
- "What Fell"; "Towards Fourteen Ways of Looking at Pohutukawa"; "Berlin", Poetry New Zealand
- "I am", Scottish Poetry Library
- Sing song. Auckland University Press. 2003. ISBN 978-1-86940-295-2.
- The Time of the Giants. Auckland University Press. September 28, 2005. ISBN 978-1-86940-342-3.
- The Last Days of the National Costume Allen & Unwin 2013
- A Boy and His Uncle. Picador. 1998. ISBN 978-0-330-36057-9.
- Musica Ficta. University of Queensland Press. 1993. ISBN 978-0-7022-2457-7.
- 100 Traditional Smiles. Victoria University Press. 1988. ISBN 978-0-86473-077-0.
- The Source of the Song (ed. Mark Williams, 1995)
- The Picador Book of Contemporary New Zealand Fiction. Trans-Atlantic Pub. November 1996. ISBN 978-0-330-33996-4.
- The Oxford Book of New Zealand Short Stories. Oxford University Press, USA. May 5, 1994. ISBN 978-0-19-558291-8. 1st edition 1992
- Bridget Williams, ed. (April 1, 2009). Some Other Country: New Zealand's Best Short Stories. Victoria University Press. ISBN 978-0-86473-588-1.
- Susan Davis, Russell Haley, eds. (1989). The Penguin Book of Contemporary New Zealand Short Stories. Penguin Books. ISBN 0-14-011007-0.
- Goodbye to Romance. Allen and Unwin. 1989. ISBN 978-99901-629-3-6.
- Alistair Paterson, Anne Kennedy, James Norcliffe, Stephen Oliver (2004). Poetry New Zealand. Brick Row.