What is an author of fables called?

There isn't a specific word for an author of fables.

However, you can refer to them as a:

* Fabulist: This is the most common term used for someone who writes fables.

* Storyteller: This term is more general and can apply to anyone who writes or tells stories.

* Moral writer: This term emphasizes the moral lesson in fables.

You can also simply call them the author of the fable.