Uber has suspended its autonomous vehicle programme across the United States and Canada after a woman crossing a street in Arizona died after being hit by a self-driving car.

The incident in the Phoenix suburb of Tempe marked the first fatality from a self-driving vehicle, which are being tested around the globe, and could derail efforts to fast-track the introduction of the new technology.

The vehicle was in autonomous mode with an operator behind the wheel at the time of the incident, which occurred overnight, Tempe police said.

"The vehicle was traveling 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.

The woman later died from her injuries in a hospital, police said.

The city is 18km east of Phoenix.

The vehicle involved in the incident was a Volvo, a person familiar with the matter said.

Local television footage of the scene showed a crumpled bike and a Volvo XC90 SUV with its front smashed.

An Uber spokesman said the company was suspending North American tests of its self-driving vehicles.

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

The US National Highway Traffic Safety Administration (NHTSA) and National Transportation Safety Board (NTSB) said they were sending investigative teams to probe the crash.

The NHTSA also said it was in contact with Volvo.

In Canada, the Ministry of Transportation in Canada’s Ontario province, which is overseeing Uber’s on-road autonomous testing in Toronto, said it was reviewing the incident.

"We will be following the situation in Arizona closely, and will consider what measures are appropriate as more becomes known," said ministry spokesman Bob Nichols.

On Friday, Alphabet Inc's self-driving unit Waymo and Uber urged Congress to pass sweeping legislation to speed the introduction of self-driving cars into the United States.

The legislation has been blocked over safety concerns by some congressional Democrats, and the Arizona fatality could hamper the quick passage of the bill.

Uber is among one of many technology companies and automakers, including Waymo and General Motors Co's Cruise division, racing to ready self-driving cars for public use in coming years.

Uber has been testing specially equipped Volvo XC90 crossovers in Pittsburgh and the Phoenix area.

Concerns over the safety of autonomous vehicles arose after a July 2016 fatality involving a Tesla Inc automobile.

The car involved in that incident featured a partially autonomous system that required human supervision.

Uber's vehicle, on the other hand, is considered a full self-driving vehicle where a human is not needed at the wheel.