The Uber driver, Shiv Kumar Yadav, 32, was arrested on Sunday. Police in India said he had been acquitted in a prior rape case in 2012.
The incident is yet another black mark against the reputation of the California-based firm, which, despite exploding popularity in dozens of countries, has faced consistent accusations that it flouts local regulations, sabotages its rivals and even endangers its customers.
Indian police said they were considering taking legal action against Uber for allegedly failing to conduct proper background checks on Mr Yadav.
Read more: Police arrest Uber taxi driver over alleged rape
The ban in Delhi means taxi drivers there face large fines if caught using the Uber app.
The company promised to work with the Indian authorities to craft better-defined rules for background checks on commercial transport licences.
"Our entire team's hearts go out to the victim of this despicable crime," the Uber chief executive Travis Kalanick said in a statement.
"We will do everything, I repeat, everything to help bring this perpetrator to justice and to support the victim and her family in her recovery."
An Indian woman travels in an auto-rickshaw in New Delhi, where taxi-hailing service Uber has now been banned. Photo / AP
Founded in San Francisco in 2009, Uber allows users to hail taxis from their smartphones, and to track their cab as a moving dot on a map.
Following a recent round of investment, the firm is now valued at US$40 billion (NZ$52 billlion).
Yet the company has faced legal action in Germany, angry protests in France and demonstrations in other European capitals by cab drivers who claim it undercuts their business and breaks local regulations on taxi licensing, insurance and safety.
This week, the company's UberPop app was banned from taking bookings in the Netherlands, after the country's Trade and Industry Appeals Tribunal found it broke a law requiring cab drivers to obtain a special licence.
Indian opposition activists protest after a woman was allegedly raped by an Uber driver. Photo / AP
Uber recently halted operations in Las Vegas after a Nevada judge granted a temporary injunction against the firm for failing to adhere to state licensing rules.
Uber has a policy of not hiring any driver with serious driving violations or recent convictions for violent crime, sexual offences, drugs or drink-driving.
But even before Friday's incident in Delhi, the company had been accused of being insufficiently thorough in its checks.
- Independent