The accident happened in Tempe, Arizona, and pictures posted on Twitter showed the autonomous car on its side next to another vehicle which was badly dented with its windows smashed.
Despite the severe damage to both vehicles, nobody was seriously injured.
The Volvo SUV was moving in autonomous mode when the accident happened.
Uber has stopped its self-driving car pilot in Arizona while it launches a probe into the crash.
An Uber spokesman said: “We are continuing to look into this incident and can confirm we had no backseat passengers in the vehicle.”
Tempe Police said another vehicle failed to give way at a traffic signal while making a left turn and collided with the Uber SUV, before a third vehicle was hit.
The self-driving programme was launched in Arizona last December after California revoked the licence of some of the cars because it said they were not properly marked as test vehicles.
Uber said on its website that the use of the vehicles was still in its early stages.
It said: “While Uber is still in the early days of our self-driving efforts, every day of testing leads to improvements.
“Self-driving cars have the potential to save millions of lives and improve quality of life for people around the world.”
Uber has been hitting the headlines after a string of scandals including accusations it tolerates sexism after a female engineer wrote a blog claiming she was harassed by her boss.
Earlier this year its CEO Travis Kalanick was forced to apologise after he was caught on video yelling at one of his own drivers.