Drama, Tragedy, Biography, Historical Fiction
It's a play, so it falls in the category of drama. More specifically, it's a tragedy, because the heroine's choices are the cause of her own destruction. Furthermore, Shaw called it a chronicle play, meaning that he wanted to document the life of Joan. This is just another way of saying that it's a biography. Last but not least, it's historical fiction, or maybe historical drama would be more accurate. In any case it's based on historical people from and past events. Shaw condensed a lot of historical events and personages for dramatic effect, but the core story is still there.