Its chief executive Dara Khosrowshahi tweeted: "We're thinking of the victim's family as we work with local law enforcement to understand what happened."
The tragedy has caused a global stir - and raised fresh questions over whether the technology is safe enough to be used.
While New Zealand has been promoted internationally as a "test-bed" for the technologies, the Ministry of Transport and the NZ Transport Agency was still reviewing transport legislation to clarify the legality of testing of driverless cars here.
That would specifically consider the issues of liability associated with testing - but would not consider liability for general use.
Meanwhile, there had been some instances of the innovation already in New Zealand.
Last year, Ohmio Automotion announced plans to start producing self-driving vehicles here after launching driverless buses in Christchurch.
Following this week's tragedy, University of Auckland computer science senior lecturer Dr Paul Ralph said it was "critical" to use perspective.
"People are using this incident to dismiss driverless cars as unsafe. Human drivers have killed hundreds of thousands of people," Ralph said.
"A driverless car has killed one. Moving to autonomous vehicles as quickly as possible is still the best way to reduce automotive collisions and their enormous cost in money, time and human life."
Ralph said that, if Uber knew that its autonomous vehicles were running red lights and did not take reasonable steps to correct the mistake, the company should be held criminally responsible for the woman's death.
"The individuals who ignored the problem should be held personally, criminally responsible - they might be charged with vehicular manslaughter or negligent homicide."
Ralph believed research on the technology should be funded by governments and carried out by expert researchers in public-private partnerships.
"But national governments, including New Zealand's, remain unwilling to invest in innovation at the scale demanded by the 21st Century."
Other experts have also weighed in.
Michael Cameron, author of an upcoming Law Foundation report on driverless vehicles in New Zealand, argued driverless vehicles would be safer than the human-controlled vehicles.
"Some regulation is necessary, but any regulation that slows down the adoption of driverless technology will likely cost many more lives than it saves."
Cameron noted how, in 1896, 44-year-old Bridget Driscoll became the first recorded pedestrian to be killed by a motor vehicle.
"And in 2018, it appears that 49-year-old Elaine Herzberg has tragically become the first pedestrian to be killed by a driverless vehicle.
"Back in 1896, the nascent motor vehicle industry managed to avoid a regulatory backlash from the Driscoll tragedy. But these are different times."
There had already been calls for tighter regulations by the director of Consumer Watchdog in the US, Cameron said.
"The irony is that, this time around, we actually have a technology that is safer than the existing technology it will replace."
"The fact the vehicle wasn't technically driverless and had a supervising driver constantly ready to take over is a detail likely to be lost in the response, but it is extremely important.
"While we won't know for sure until the investigation is complete, the supervising driver would have been a highly skilled professional, and he or she also failed to avoid Ms Herzberg."
Professor Hossein Sarrafzadeh, of Unitec's High Tech Research, said that, with the rapid emergence of driverless cars and autopilot technology, such an incident was likely to have occurred sooner or later.
"The cause of the accident has still not been determined and I am sure there will be greater emphasis on the safety of these systems following the investigation, however, it is important to take this single event into context when considering the overall safety of these cars, particularly in comparison to human-operated vehicles," he said.
"There is no doubt that more work needs to be done to make autonomous cars safer.
"Equipping roads with sensors, wearable technologies, AI and machine learning are just some of the technologies that will need to be employed to increase the safety and security of these technologies.
"We need to hold any judgment until investigations have been undertaken and videos and other data relating to the accident have been analysed. Innovation will continue."
