Four other people were injured in Hyderabad, the state's capital, when a house's boundary wall fell on a neighboring house, which collapsed with the impact, police officer Gaja Bhopal Rao said.
The first house to collapse in Hyderabad was in a hilly area of the city where the soil was loosened by more than 25 centimeters (9.8 inches) of rain in the past 24 hours, said Police Commissioner Anjani Kumar. That left eight people dead, AP reported.
Five other people were killed in two other house collapses in the city, Kumar said. Two other people were swept away by flood waters elsewhere in the state.
The rain washed away part of the highway linking the city to the airport.
Thirty cars and trucks were washed away when a lake in the city overflowed, district administrator Amoy Kumar said.
The heavy rain in Hyderabad, caused by a deep depression in Bay of Bengal, broke a record set 20 years ago. It caused flooding in low lying areas of the city, where authorities used boats to evacuate people.
More than 9.6 million people across South Asia have been affected by severe floods this year, with hundreds of thousands struggling to get food and medicine.
About 550 people have died in India, Bangladesh and Nepal, while millions have been displaced from their homes since the flooding began in June.