A woman died of her injuries after being struck by an Uber self-driving vehicle in Arizona, police say, prompting the ride-hailing company to suspend its autonomous-vehicle programme across the US and Canada.

Monday's accident in Tempe, Arizona, marked the first fatality from a self-driving vehicle, which are still being tested around the globe, and could derail efforts to fast-track the introduction of the new technology in the US.

At the time of the accident, which occurred on the night between Sunday and Monday, the car was in autonomous mode with a vehicle operator behind the wheel, Tempe police said.

"The vehicle was travelling northbound ... when a female walking outside of the crosswalk crossed the road from west to east when she was struck by the Uber vehicle," police said in a statement.

A spokesman for Uber Technologies Inc said the company was suspending its North American tests.

In a tweet, Uber expressed its condolences and said the company was fully cooperating with authorities.