Tropical Cyclone Fani has barrelled into eastern India, bringing down trees and power lines and "extensively" damaging the tourist town of Puri.
But there were no early reports of casualties with a million people evacuated before it made landfall.
Tropical Cyclone Fani, the strongest to hit India in five years, spent days building up power in the northern reaches of the Bay of Bengal before it struck the coast of the state of Odisha.
Howling winds gusting up to 200km/h whipped trees, uprooting scores, and driving rain impacted visibility, while streets were deserted in the state capital Bhubaneswar and Puri.
Cyclone tracker Tropical Storm Risk put Fani as a powerful category four storm on a scale of one to five. The IMD said the storm was now weakening.
Close to 60km inland, winds brought down electricity poles in Bhubaneswar, where authorities had ordered the airport to stay closed.
People packed into shelters, spreading mats to wait out the storm, television and social media showed.
More than 600 pregnant women were shifted into safe locations, with nearly 500 ambulances on standby. Some 242 medical institutions had been provided with power back-up, government authorities said.
In neighbouring Bangladesh to the north, authorities have begun moving 500,000 people from seven coastal districts, a government minister said.
The storm is due to hit Bangladesh late on Saturday and ahead of that, ports have been ordered shut, a government official said.
Neighbouring West Bengal also planned to shut down the airport at Kolkata, its state capital.
India's cyclone season can last from April to December, when severe storms batter coastal cities and cause widespread deaths and damage to crops and property in both India and neighbouring Bangladesh.
But recent technological advances have helped meteorologists predict weather patterns more accurately and prepare.
A super-cyclone battered the coast of Odisha for 30 hours in 1999, killing 10,000 people.
In 2013, a mass evacuation of nearly a million people likely saved thousands of lives.
Cyclones typically quickly lose power as they move inland.