The rains have killed 25 people in the island nation of Sri Lanka, most of whom drowned, while landslides injured five, officials said.
Sixteen people were killed in Tamil Nadu, state disaster management minister KKSSR Ramachandran told a news conference.
Many parts of the state capital, Chennai, which is India's auto manufacturing center, were waterlogged and government officials used pumps to drain some communities that had been stranded waist deep.
Thousands of people in low lying areas were moved to safety, officials said.
Many schools and colleges in Tamil Nadu remained closed while some train services were still suspended. India's northeast monsoon usually runs from October to December, bringing heavy rain, particularly to the south.
