
Cyclone Gaja, which packed winds of up to 120 kilometres per hour, had barrelled into Tamil Nadu state after hitting the coast on Friday.
Thousands of trees were felled by winds that destroyed homes and hundreds of thousands were forced to flee to shelters.
Cyclone 'Gaja' makes landfall in south India, kills 11 people
"So far 20 men, 11 women, and two children have died due to the cyclone," said an official with the state disaster management authority, who asked not to be named as he was not authorised to speak to media.
"As of now 177,500 people are housed in over 351 camps. Thousands of trees have been uprooted and livestock has also been badly affected," he told AFP.
Chief Minister Edappadi Palaniswami, who has announced compensation of $14,000 each to the families of victims, said most deaths were caused by flooding, house collapses and electrocution.
Hundreds of emergency workers have been pressed into service to restore roads and power cables, as the full scale of the disaster becomes clear.
Cyclone batters eastern India, 300,000 evacuated
A Navy helicopter and two ships have joined relief efforts in the state, the local government said.
India's weather department said the cyclonic depression had moved westwards Saturday into the neighbouring Kerala state before continuing into the Arabian Sea.
Gaja is the second major storm to hit India's east coast in recent weeks. Cyclone Titli battered Odisha state in October, killing at least two people.
Storms regularly hit southern India between April and December. Last year, Cyclone Ockhi left nearly 250 people dead in Tamil Nadu and Kerala states.
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