The blog Den of Geek, by way of introducing a DVD release of the movie Monsters, joins a long line of commentators who credit Ray Bradbury with inventing the "primeval creature causes destruction in the modern world" subgenre. The justification for this claim is Bradbury's short story "The Fog Horn", once and famously filmed as The Beast from 20,000 Fathoms.
The claim is perhaps slightly exaggerated, in that many of the key elements of this subgenre originated with the movie amd are nowhere to be found in Bradbury's original story. However, any grace and pathos typically found in such movies are most definitely to be found in "The Fog Horn". And it's but a short step from the central image in Bradbury's story to the imagery of The Beast from 20,000 Fathoms, which was achieved chiefly through the efforts of Bradbury's lifelong friend, Ray Harryhausen.
Read more about Bradbury's contribution to The Beast... on my page for the movie, here - and other posts relating to the Rhedosaurus here.