Children's Literature (definitely), and Folklore, Legend, and Mythology
Where do you suppose you would find this book in a bookstore? In the kids' section! Plus, it's a picture book, the language is relatively simple, and people have been reading it to children for over forty years. So, it's not hard to see that yes, this book belongs in the Children's Literature genre. But it fits at least one other category, too: Folklore, Legend, and Mythology.
Despite having been written in modern times (1975), Strega Nona feels like an old tale. And plenty of people have mistaken Strega Nona herself for a character from Italian folklore of old. Tomie dePaola reports that more than once he's been approached by people who have told him they're glad that someone is finally telling the old Strega Nona tales again (source). To which dePaola thought, "Again?" As far as he knew, he had made Strega Nona up.
A bit of research confirmed for dePaola that he hadn't plagiarized his beloved character and that she was, indeed, an original creation. But setting the story "a long time ago" (7), including magical elements like the pasta pot, and incorporating a few overarching lessons into the text have solidified Strega Nona's place in the land (and genre) of folklore.