The storm was centred in the Bay of Bengal, 200 kilometres (125 miles) east of the city of Chennai, with winds of about 55 kilometres per hour, the India Meteorological Department said.
Forecasters warned that the "cyclonic storm" would make landfall early on Wednesday.
"We have declared a holiday in all the schools, colleges, government offices in five districts of Tamil Nadu. Fishermen have been warned not to go out into the sea," Jayraman, a government administrator who goes by one name, told AFP.
He said the storm was predicted to intensify before hitting the coast near Chennai with wind speeds of up to 100 kilometres per hour.
The weather department in its latest warning said a "storm surge" was likely to inundate five coastal districts, having an estimated population of 600,000.
Authorities warned that was a possibility of extensive damage to power and communication lines. They were preparing helicopters and boats to be ready for any emergency.
Ravi Babu, a senior disaster management official in the state, said that besides existing cyclone shelters, schools and community halls had been identified to serve as potential relief camps for evacuees.
Neighbouring Sri Lanka on Tuesday allowed thousands of people who had been evacuated to return to their homes after the storm, which had been expected to hit the island, changed its course and moved towards India.
Copyright AFP (Agence France-Presse), 2012