The killing has been denounced by marine conservation group Sea Shepherd as a "brutal and badly mishandled" massacre, and the largest single hunt in the Danish territory's history.
The organization said a super-pod of 1,428 Atlantic white-sided dolphins was corralled by speed boats and jet skis onto Skálabotnur beach on the island of Eysturoy, where they were then killed.
The Faroe Islands are an autonomous territory of the Kingdom of Denmark, lying about halfway between Scotland and Iceland in the Atlantic Ocean.
The annual whale hunt, or grindadráp in Faroese, has been a part of local culture for centuries -- but it usually involves the hunting of pilot whales. Although it has long been criticized by animal rights groups, locals have defended the practice.
41-year-old Kristian Petersen, who is originally from the Faroese town of Fuglafjørður but now lives in Denmark, said he began participating in whaling at the age of seven -- but in his village, dolphins were never targeted.
"I have experienced that firsthand and also participated a bit," Petersen told CNN. "As long as it has been for food only, I have supported it. But this recent catch that was this weekend, I'm against how it went on.
Petersen is one of several whaling supporters who have condemned Sunday's killing, saying there were "so many errors," including pursuing a large flock and prolonging the dolphins' suffering by not having enough people on the beaches to kill them.
In recent decades, the practice has come under strict regulation from the Faroese government, with guidelines for the authorization of hunts and how they should be conducted.
Many, including Petersen, have questioned the legality of Sunday's killing, with allegations that the local foreman, who is involved in regulating whaling in the area alongside the district administrator, was not informed in line with regulations. Sea Shepherd also claimed that several of those involved did not have the required licenses to participate.