Genre is never something that can be cleanly simplified to a single classification—a story or novel can and usually does fit multiple genres, all at the same time. "The Yellow Wallpaper" is no different.
First, I think it's safe to classify it as a work of epistolary fiction. Epistolary fiction is fiction which is told through a sequence of documents, usually produced by characters within the story (to give an example, one of the most famous works of epistolary fiction is Bram Stoker's Dracula). Given that "The Yellow Wallpaper" is told as a sequence of diary entries written by its main character, it qualifies as such.
In addition, given its thematic content, we can classify this short story as both a work of feminist literature and a work of psychological fiction. These are just a few examples of classifications which we can apply.