Witnesses contacted police after spotting the fox being surrounded by the dogs at Winton Bank close to the A684 near Northallerton on Saturday shortly before 3pm. A motorist also contacted police after she had run over a fox in her car and told officers she saw the animal being set upon by hounds.
It is understood police are investigating the possibility the dogs chased the fox into the road.
The carcass of the fox has been handed to the RSPCA to establish a cause of death. Insp Mike Harvey from North Yorkshire Police said an investigation was under way, but it is not thought anyone has been questioned at this stage.
Insp Harvey added: "If any offence is detected, then we will investigate it fully before handing details over to the Crown Prosecution Service, which will then decide whether the case should progress to court.
"Inquiries are progressing and officers would like to hear from anyone who has information about the incident."
An RSPCA spokeswoman said she was aware that prosecutions had been brought against hunt members in England for the illegal killing of foxes since the Government's controversial ban on hunting became law last February.
Hounds can, however, be used to follow a scent and to flush out a fox. The fox can then be killed by a bird of prey or shot – if only two dogs are involved.
The Yorkshire Post contacted the secretaries of several North Yorkshire hunts yesterday who all said they knew nothing about the death of the fox.
Anyone with information can contact police on 0845 6060247.