Blame it on It may be due in part to the popularity of "The Frog Prince," which is the first fairy tale in the collection of the Brothers Grimm, and is one of a number of folktales of Frog Kings. The idea seems to have caught on from there - it entered into contemporary fantasy through works like J. R. R. Tolkien's The Lord of the Rings, where Frodo threatens Samwise Gamgee:

If you don't, if you even breathe a word of what you've heard here, then I hope Gandalf will turn you into a spotted toad and fill the garden full of grass-snakes.

The idea of transformations in general are rampant throughout many folktales, and before that legends and myth, attributed to both witches and gods. For example, in Book X of the Odyssey Circe transforms Odysseus' sailors into pigs, and The Metamorphoses of Apuleius are often called "The Golden Ass" because the protagonist is transformed into a donkey.

[/edit] A caveat to this answer, because as u/itsallfolkore adds the way I've worded it could be misleading. As the multiple variations on witches turning people into frogs/toads I linked above shows, there was a folkloric tradition of witches-transforming-people-into-frogs throughout Europe which probably dates back centuries, and was part of the much broader tradition of witches-transforming-people-into-<insert object/animal here>. These folktales were later collected, published, translated, and popularized broadly in the 19th century, which took the centuries-old witch-transformation-frog stories and made standardized editions of those tales widely accessible - case in point, the Brothers' Grimm, whose Children's and Household Tales often start with the Frog Prince/King story and which saw massive popularity in Victorian England led to the wide dissemination of the idea, which was adopted by fantasy literature. So it's not that the Brothers' Grimm made it all up, or that they alone are responsible, but their publication of that story in that format appears to be a place you can point to as the witch-transformation-frog bit transitioning from regional folklore into mass literary consciousness.