The dolphins were discovered in two separate incidents by members of the public, and reported to the Department of Conservation.
One was found near Banks Peninsula, and the other near Greymouth, on the West Coast.
Ministry for Primary Industries compliance investigations manager, Gary Orr, said the deaths could be caused by humans.
"Our investigation will look to identify everyone who was fishing in the areas prior to the discovery of the dolphins," Orr said.
Orr said the penalty for causing the death of a Hector's Dolphin and not reporting was up to $100,000 for a commercial fishing operation, and $10,000 for an individual.
Hector's Dolphins are considered an endangered species, and a range of restrictions are in place to protect them from fishing accidents.