Tamil Nadu and Andhra Pradesh states in the south and Odisha in the east braced for flooding as authorities issued warnings for Tropical Cyclone Michaung.
It is likely to hit the southern coast on Tuesday with maximum sustained winds of 90-100km/h and gusts up to 110km/h, the Indian Meteorological Department said on Tuesday.
The storm could make landfall on Tuesday afternoon close to Bapatla in Andhra Pradesh state, said the head of the department, Mrutyunjay Mohapatra.
The Andhra Pradesh state government shut schools on Monday while authorities in Tamil Nadu declared a public holiday in four districts that are likely to bear the brunt of the downpours. In the eastern state of Odisha, a number of districts experienced heavy rain, which authorities said could intensify on Tuesday.
The Hindu newspaper reported officials evacuated nearly 2000 people from coastal and low-lying villages in Andhra Pradesh state, with instructions to move more than 7000 more to safer areas.
In Tamil Nadu's capital, Chennai, strong rains submerged roads and cars in knee-deep waters that flooded parts of the city as members of India's National Disaster Response Force began evacuating those in low-lying areas.
Videos showed water streaming onto the city's airport tarmac, forcing authorities to shut it down and divert more than 30 flights while about 70 were canceled, the Press Trust of India news agency reported.
India's weather department said parts of Tamil Nadu and Andhra Pradesh were likely to see more than 200mm of rain over the next 24 hours.
Authorities in Tamil Nadu over the weekend had deployed their own disaster response force and set up nearly 5000 relief camps in coastal areas.