Six lambs had already been killed by the dog before the farmer intervened to prevent further loss of life at a farm in the Hebden Bridge area on Wednesday.
Farmers are legally allowed to shoot dogs that are worrying their stock as long as they hold a valid firearms licence.
There have already been several incidents involving dogs attacking sheep in Yorkshire this spring.
In February the owner of a husky had to pay veterinary bills after the dog mauled two sheep in a field in Dunnington, near York, having run through an electric fence to gain access.
The same month a woman ran away from the scene after her dog attacked sheep in the village of Drax, near Selby, despite being challenged by a farm worker.
And in March a pregnant ewe had to be put down after being mauled by a dog near Danby in the North York Moors.
Dogs should always be kept on leads around livestock and owners should be aware that they have a natural instinct to chase, even when usually obedient, and may not respond to calls to return.
Anyone with any information on the Hebden Bridge attack should contact West Yorkshire Police quoting reference number 13210196782.