The suspect was held in his home town in Uttar Pradesh where his car was earlier found abandoned. He will be brought before a New Delhi court on Monday, said Madhur Verma, deputy commissioner with the Delhi police.
Police opened a rape investigation after the 26-year-old woman reported that she had been sexually assaulted and beaten after hailing a ride home with the Uber driver from a social event late Friday in south Delhi.
Verma said the police would consider legal action against Uber for violations including a failure to check whether the driver, named as Shiv Kumar Yadav, had a clean police record and the lack of a satellite location device in his car.
"Every violation by Uber will be evaluated and we will go for legal recourse," said Verma, saying police would take legal advice before opting to press a criminal or civil case.
Uber has faced critical news coverage over its driver screening in the United States, and has apologised for comments by an executive who suggested "digging up dirt" on journalists investigating the firm.
That has not stopped the San Francisco-based firm from raising investment that values it at $40 billion, reflecting the perceived potential of its expansion into high-growth markets like India.