The 26-year-old woman reported that she had been sexually assaulted and beaten when she got a ride with the Uber driver after a social event late on Friday in Vasant Vihar, south Delhi.
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.
Police have deployed four teams of five members each to trace the 32-year-old driver, identified as Shiv Kumar Yadav, who has switched off his mobile phone since the incident to avoid being traced.
The driver dropped the woman home after attacking her and warned her not to inform the authorities.
She managed to note down the driver's number and take a photograph of his car, which was later found in the northern state of Uttar Pradesh.
"Our first priority is to arrest the driver and collect the evidence in a scientific manner, so that the victim can get timely justice," Madhur Verma, deputy commissioner with the Delhi police, told Reuters.
Delhi recorded the highest number of rapes in India in 2013, according to the latest National Crime Records Bureau data, earning the dubious distinction of being India's "rape capital".
Police attribute the rise in reports to more women coming forward due to greater public awareness following the high profile gang rape and murder of a 23-year-old woman on a bus in December 2012.
San Francisco-based Uber said in a statement on Sunday it had suspended the driver following the allegations, in line with company policy, and would assist the police.
"Safety is Uber's highest priority and in India, we work with licensed driver-partners to provide a safe transportation option," said Uber spokeswoman Evelyn Tay.
Delhi police's Verma, however, said that there has been "a lot of negligence in terms of security" on the part of the company.
"There is no GPS (global positioning system) installed in the vehicle and there was no background check or driver verification done with the police."
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@lol: It takes a sick man to find humour in rape,be it in Pakistan or India.I am from Pakistan but i cant get myself to score brownie points on this tragedy,have some mercy my friend,karma is cruel!
in pakistan there is no uber ...... this shows pakistan has taken steps to protect females from honor killings and gangraped by feudal lords :)