Police in the city of Tempe said on Monday that the vehicle was in autonomous mode with an operator behind the wheel when the woman walking outside of a crosswalk was hit.
Sgt. Ronald Elcock says in an email that the accident happened overnight but did not say whether it occurred on Sunday night or Monday morning.
The woman died of her injuries at a hospital and her name was not made public.
Uber has been testing the self-driving vehicles in Tempe and Phoenix for months.
Uber says on Twitter that it is “fully cooperating” with the investigation and expressed condolences to the family of the victim.