Sea Shepherd captain Jessie Treverton was on Friday fined 5,000 kroner (€670, $710) by a court in Torshavn for causing "unnecessary suffering" to a pod of white-sided dolphins that the group claims it was trying to protect from hunters.
The group's vessel was trying to steer the dolphins away from one of the beaches where sea mammals, usually pilot whales, are killed during the hunt.
"If the law applies to me then it surely must also apply to the Faroese people," Treverton, from Britain, said in a statement.
"A legal precedent has been set, driving dolphins is against Faroese law," she added.
The group's campaign leader in the Faroes, Geert Vons, told AFP that it had to receive the whole ruling before deciding how to proceed with any legal challenge to the hunt.
A spokeswoman for the Faroese government denied the ruling showed that the whale hunt violated the territory's animal welfare law, and said it merely reflected the "unnecessary" suffering caused to the animals by the activists, and that Sea Shepherd lacked the relevant permit.
During the hunt, the cetaceans are driven by a flotilla of small boats into a bay or the mouth of a fjord before being killed by hand -- a practice that many locals defend as a cultural right.
The whale meat and blubber are consumed by locals and considered delicacies.
The Faroe Islands are a self-governing archipelago belonging to Denmark in the North Atlantic Ocean.