Rains after drought
The worst hit areas were Chongqing municipality, with at least 31 dead and 8,000 collapsed houses, and Hunan province, where 10 people died.
Chongqing's authorities have relocated more than 85,000 people.
Only a month ago several of the same provinces were suffering from the worst drought in a century to hit southwest China.
Up to 157 millimetres of rain had fallen in parts of the region from late Wednesday to Thursday afternoon, Xinhua said.
The storms were caused by a heat wave from the south colliding with a northern cold front, reports said, citing meteorologists.
An official in Xinmin township told AFP that older houses suffered "very serious" damages, although newly built brick homes were also damaged.
Power was cut in several areas, many roads in the region were blocked by flooding, and bridges also suffered damage.
Chongqing, a province-sized municipality, has a population of more than 30 million people.