The incident happened at just after 2.15pm at a farm in Moreton-on-Lugg and the Fire Service's control room took five 999 calls in relation to the fire.
On arrival, two crews from Herefordshire and the Water Carrier from Leominster Fire Station found that the fire had taken hold of the building.
Station Commander Neil Pigott, who was officer in charge of the incident, said: "The fire involved a hay store and stable with a floor area of approx 100msq. The building has been completely destroyed as has the hay and fodder within.
"It is almost certain that this fire was started deliberately and the culprit is a danger to themselves and others. I would urge anyone with information that could assist in identifying those responsible to contact Crimestoppers on 0800 555 111."
The number of fire crews at the scene has been scaled down but the stop message has not yet been given.