The sheep, including 11 ewes and three lambs, were found dead at 9.15am on Thursday in a field at the top of Golden Hill, Huttons Ambo, close to the A64.
Officers believe the they died after being chased around the field by dogs, causing them to become distressed and run into boundary fences.
North Yorkshire Police has appealed for anyone who witnessed the incident to come forward.
Anyone with information is asked to contact police on 101, quoting reference number 12170099759.