The impact of the collision in Assam state late Saturday derailed the engine but no passengers were injured, regional railways spokesman P.J. Sharma told AFP.
Another elephant was seriously injured in the accident, he added.
The elephants were part of a larger herd migrating through the hilly forest state, where train tracks cut across elephant corridors that act as transit routes for the wandering animals.
India has nearly 30,000 elephants and Assam is home to its largest population of the Asian variety, an endangered species.
Railway authorities have introduced speed restrictions on some routes that are designated elephant corridors. It was unclear whether this latest accident occurred in one of these zones. But the interventions have not stopped accidents. Five elephants were killed in December in a train collision near a tea plantation in Assam.
Deforestation and construction activity near their habitats force elephants to stray further afield for food, often bringing them into conflict with humans.
An estimated 60 elephants died in 2017. Many of the deaths were caused by electrocution, as farmers erect electrified fences around their fields to keep wild animals away.