Puducherry had been hit by the heaviest 24-hour rainfall in 30 years, India's weather office said on social media on Sunday, Reuters reported.
The cyclone left parts of the southern city of Chennai inundated. Flights from the city were temporarily suspended on Saturday, but had resumed as of early Sunday morning, India's airport authority said.
Visuals on local media showed gusty winds and heavy rainfall with roads submerged and boats being used to rescue people.
The Indian army was running relief operations in Puducherry for people in the eye of the storm, while rainfall eased in Chennai.
In Sri Lanka, 16 people were killed, with heavy rains affecting a total of 138,944 families, the latest data from the Disaster Management Centre in Colombo showed.