That depends on how you define the genre of "Fantasy", and where you put its beginnings. The beginnings of Undead creatures in fantastic literature can be seen in Mary Shelley's 1818 opus Frankenstein, often considered to be the first science fiction work, and science fiction and fantasy are often combined in a single genre. Slightly later, we have vampires being introduced into popular consciousness with Bram Stoker's 1897 Dracula. If we go into the fantasy genre, we find that one of the earliest fantasy writers was George MacDonald, and in his 1895 story Lilith, we see several "undead" characters, such as the ghost Mr. Raven, as well as the titular "Lilith", who is the Biblical Adam's first wife, who is still around and serves as the antagonist in the story.

Based on these examples, I would say that the use of undead characters in fantasy is almost as old as the genre itself.