Jaipur, capital of the northwestern state, was the worst-hit, with at least eight dead in the monsoon rains, reported to be the heaviest in more than three decades, the Times of India reported.
The BBC put the death toll at 20.
The rains began as a drizzle Tuesday but by Wednesday night had become torrential.
Dholpur and Dausa districts neighboring Jaipur were also badly affected, the Times said.
At least 6.7 inches of rain had been recorded in the Jaipur area, a rarity as Rajasthan is home to the Thar Desert.
Jaipur officials closed junior grade schools Thursday. Rail and road transport remained disrupted in the state and thousands of people were forced to leave their homes.
Officials said at least 20,000 food packets had been distributed to those affected by the bad weather, while nine relief teams were surveying the damage. Several low-lying areas in Jaipur remained underwater.