The rainfull has also shut down factories and caused major travel delays.
Weather experts say the seasonal northeast monsoon is responsible for the flooding in the city of Chennai, home to at least six million people.
The army has been deployed to rescue thousands of stranded people, and the death toll is expected to rise.
India's weather bureau says heavy weather conditions are expected to continue for at least another three days.
Many parts of Tamil Nadu lack adequate drainage, further complicating the effects of the floods.
Rakesh Kamal, from India's Centre for Science and Environment, says the heavy flooding is a sign that India must do more to prepare its infrastructure for such natural disasters.
"The wetlands have been converted into sewage canals. That becomes a really major issue for the city to even handle it. Chennai, even on a normal course, is only around six meters above sea level but its natural lakes helped let the water drain out in the past. But with them being closed, we'll only be seeing more and more rainfall like this happening in the future. We better start worrying about it. We have to prepare our infrastructure and also be ready with our climate change plans."
Prime Minister Narendra Modi has blamed climate change for the rain, injecting urgency into the debate at global climate talks in Paris and highlighting the vulnerability of tropical nations like India to extreme weather.
Mr Modi has ordered rescue teams and paramilitary forces to launch an extensive relief and rescue operation in Chennai.
Three teams from the National Disaster Response Force from New Delhi left for Tamil Nadu with a plane-load of relief material.
Alok Bhatnagar is the naval officer-in-charge of Puducherry and Tamil Nadu.
"INS Rajali and INS Parandu, our naval air stations, have put their helicopters and remotely piloted aircraft ready for operations in support of our relief operations that we are doing here in Chennai."
Chennai, India's fourth most-populous city, is a major car manufacturing and IT outsourcing hub.
Many major companies have told their workers to stay at home.
The floods have also affected the city's international airport with many flights cancelled.
Hundreds of divers and army rescue teams have also entered flooded homes, taking the injured to hospitals.
Authorities say more than a million people are affected, with some residents criticising the slow response of the relief teams.
"This time maybe due to the government's lack of preparation before the monsoon. Waterlogging everywhere, if you see from this side to that side, from that side to this side - everywhere it is water. People are finding it very difficult to find a shop to buy groceries. Everything is closed. From last night, no power."
Weather experts had warned late last month the remnants of Typhoon Marilyn, which had formed near the Philippines, could turn into a tropical depression and bring heavy rains to India's east coast and compound the effects of the seasonal monsoon.
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