Any image that references a work of fine art, whether classical or modern. If the image just has the appearance of being painted but may or may not reference a specific piece of fine art, use painterly. For the actual fine art being referenced use fine art.
On Pixiv these types of images are usually tagged 名画オマージュ
(meika omaaju, masterpiece/famous picture homage)
On Danbooru, the name of the painting is usually put as a copyright, and the original artist is not added as a tag.