A driver from Ulrome, who did not wish to be named, saw the rats under a tree on the stream bank at the Bracey Bridge picnic site, off the A614 Bridlington to Driffield road.
He said between 15 and 20 rats can be seen at any one time, about 50 yards from a snack stand – but other people have reported seeing about 100.
He said: "You're used to seeing the odd rat, but this is a thriving colony."
But when he reported the issue to animal health officials of East Riding of Yorkshire Council, he was told nothing could be done about it, because people used the layby.
But an East Riding of Yorkshire Council spokesman said pest control treatment started at the site last Wednesday and would continue for as long as necessary to solve the problem.
Members of the public have also been seen shooting the rats.
Andrew Thrippleton, part-owner of Classic Catering, of Beeford, who operates the snack stand at the site, said: "This is the first time in 14 years I've seen anything like this."
He believes the problem has been caused by animal feed being dumped in the area over the winter.