Local residents found the carcasses of the elephants in a forest in the state's Nagaon district and alerted the forest department officials, who in turn recovered the bodies.
Assam Forest Minister Parimal Suklabaidya said the carcasses were sent for postmortem, and an investigation is underway.
"This is a very sad incident, such incident has never occurred in the forests of Assam. Today in the afternoon during rainfall, a thunderstorm occurred and it was so intense that 18 elephants died in the forest," he added.
India is home to over 50% of the Asian elephants but their population has declined in recent years due to habitat loss, poaching for their tusks, and erratic enforcement of forest laws.