What genre is the novel The Color Purple?

Well, first of all The Color Purple falls under the broadest genre of fiction.  The three primary genres are poetry, drama, and fiction.  Once assigned a broad genre, a work is then subcategorized:  in this case, the subgenre is the novel (as opposed to the short story, for example.)  The novel follows certain conventions (expectations), such as the rising action, climax, and denoument (falling action), to which Walker's novel adheres.

If you were to further subcategorize her work, you might then classify The Color Purple into African-American fiction or feminist fiction.  It is also possible to think of this work as a mildly historical novel, as the conflicts the characters contend with are based in reality (the aftermath of slavery, racism, poverty, etc., in America.)  Another way to understand the genre is as epistolary, which means written letters, as the entire novel is told through the correspondences of Celie to God. 

If you were to write an essay on the novel, choose one of the sub-sub-categories to explore.  You might try to fit Walker's work into the context of other epistolary novels, seeing what conventions she adheres to and where she diverges.  You could even take a psycholanalytic approach, which would explore the ways in which Celie is affected by her environment and experiences.