There are multiple examples of the supernatural in Gilman's short story The Yellow Wallpaper. The unnamed narrator tells readers that the "colonial mansion" she is staying in is a "haunted house." She mentions that her husband, John, is greatly superstitious--ignoring her "mentionings" of anything which cannot be justified and verified.
Outside of the narrator's "mentionings" about the house and her husband, readers first come into contact with the "spirits" of the wallpaper when described. The paper has "bulbous eyes" which watch her and crawl over the paper. Later, the narrator's fears regarding the wallpaper compound; she feels as though a woman has come to live behind the paper, "stooping down and creeping about behind that pattern."
After telling her husband about the lady behind the paper, the narrator begins to see much more moving behind the paper. Later when Jennie comes in, the narrator catches Jennie touching the paper. Jennie claims that the paper is staining everything which touches it.
In the end, the "movement" of the paper is certainly supernatural. The narrator swears that the paper moves. Under a clear and normal mind, wallpaper cannot move. It can only be something "supernatural" which the narrator defines.