Cyclone Mahasen made landfall on the coast of Bangladesh on Thursday, killing 14 people. Warnings have been downgraded as the storm lost strength.
A storm surge caused some flooding along the coast at high tide and thousands of huts were destroyed by torrential rain and wind, but the extent was not as bad as had been feared.
Chittagong district administrator Mohammad Abdullah said a million people spent the night in cyclone shelters, schools and colleges along the coastline.
Neighbouring Myanmar (Burma) also appears to have been largely spared.
The storm is now moving into northeastern India.