The decision follows an accident in which Elaine Herzberg was killed crossing a road in the city of Tempe when she was struck by one of the company’s autonomous vehicles.
When the state's governor wrote to the firm confirming the ban he said that there had been an "unquestionable failure" to make safety the top priority.
Safety protocols have been queried as a video of the incident shows that the operator was looking down, rather than directly at the road, for about five seconds before the accident.
Doubts have also been raised by the dashcam video Uber provided to the police. Other road users, who uploaded their own dashcam videos, show that night time visibility was far better than Uber suggested.
Plenty of companies have also said that their technology would have handled the situation, while Velodyne - the firm that designed the collision-avoidance sensors that Uber employs – is said to be "baffled" by the accident.
It’s been a difficult few weeks for the proponents of self-driving what with the contradictions around the Uber accident and now with the news that a Tesla vehicle operating on Autopilot crashed in California last week.
Could the fall-out from these accidents stall the development and testing of self-driving vehicles? Fatalities like these present an unprecedented liability challenge because self-driving vehicles involve a complex system of hardware and software often made by outside suppliers.
From the events of the past few weeks could it be that autonomous vehicles are a long way from being ready for unattended use on public roads? Have the promoters of "self-driving" cars radically underestimated the complexity of the problem they are trying to solve?
The benefits of self-driving cars are clear, but are we rushing to bring this technology to market?
While it might cost more and take longer, if this technology is to be accepted worldwide then it will be crucial that accidents of this sort are investigated openly and their findings made public.
