Abani has been awarded a PEN/Barbara Goldsmith Freedom to Write Award, the 2001 Prince Claus Awards, a Lannan Literary Fellowship, a California Book Award, a Hurston-Wright Legacy Award and the Hemingway Foundation/PEN Award.
In summer 2016 a broad selection of his works has been published in Israel by the small independent publishing house Ra'av under the title "Shi'ur Geografia" (Hebrew for: Geography Lesson) edited by Noga Shevach and the poet Eran Tzelgov.