Another man was critically injured by the four elephants, who entered the village of Bhatar in West Bengal state on Sunday morning after apparently straying from their herd.
West Bengal forest minister Benoy Krishna Burman said the victims were trampled after angering the elephants by throwing stones to try to scare them off.
The male elephant died when it was hit by a tranquilliser dart fired by forestry officials summoned to help, and the other three — a female and two calves — ran away, Burman said.
Wildlife experts say encounters between humans and elephants are increasing in India’s rural areas due to the destruction of the animals’ habitat.
Last month a wild elephant went on an hours-long rampage in a town in eastern India, damaging about 100 homes, shops and other buildings.
Photos showed the bewildered animal wandering around Siliguri, about 577 kilometres (360 miles) north of Kolkata, crashing into structures, as people scurried out of the way.