The vandalism at the Cavendish Arms in Embsay, near the Bolton Abbey estate, was not discovered for around a week and it is unclear whether the hives belonged to the pub or were owned privately.
Thr fire is believed to have started between February 23 and March 2 in a field behind the pub.
PC Pete Macmillan confirmed that around 40,000 honey bees had sadly died.
Officers are checking CCTV footage from buildings in the village.
Anyone with any information is asked to contact North Yorkshire Police on 101 quoting incident number 03032021-0079.