The attack happened at 8pm in Oaro, said Sergeant Mike Western of Kaikoura police.
Mr Western said the girl was fortunate not to suffer more serious injuries. He said the jack russell had since been destroyed. "They are either angels or shockers."
He said he believed the attack was unprovoked, and occurred as the girl went to feed the animal. "It went for her, not the food bowl."
He said family pets such as labradors and jack russells were often responsible for dog bites.
The girl, from Parnassus in North Canterbury was visiting extended family in Oaro over Christmas. She had now been discharged from hospital, said Mr Western.
So why are dog breeds banned????