The victim died in hospital following the incident in Tempe last night, 18 March 2018, when the Uber car hit her while operating in autonomous mode, according to police.
An operator was behind the wheel of the vehicle at the time, but it was not carrying any passengers. The woman was walking outside of a designated crosswalk, reports claim.
Uber responds on social media
"Our hearts go out to the victim's family," said a Twitter statement from the ride-sharing company. "We are fully cooperating with local authorities in their investigation of this incident."
Uber CEO, Dara Khosrowshahi, also took to the social media platform to offer condolences. "Some incredibly sad news out of Arizona," he said. "We're thinking of the victim's family as we work with local law enforcement to understand what happened."
Uber has been testing its driverless vehicles since August 2016 in several US states, where road laws permit, as well as in Canada.
But the company has temporarily halted all self-driving operations in Phoenix, Pittsburgh, San Francisco and Toronto while the investigation into the incident continues.
Latest driverless car accident
Several accidents involving driverless cars have happened in the past few years. The first fatality occurred in July 2016, when a Tesla owner was killed after its Autopilot mode failed to recognise an oncoming lorry.
Uber has been ramping up its efforts to roll out autonomous taxis. It is developing its own fleet of cars with car brand Volvo at a facility in Pennsylvania, and recently announced that auto giant Daimler will use its software in vehicles.
The company's app allows users users to order a taxi on-demand, usually at a cheaper price than local options, and takes the payment straight from a stored bank card so cash is unnecessary.
Since it set up by Kalanick and Garrett Camp in 2009, Uber has transformed the taxi industry and started a ride-sharing revolution that has caused controversy worldwide.