The world-famous company has decided to suspend the tests in cities across North America after a 49-year-old woman was hit by a car and killed as she crossed the road.
Following the tragic news, Carla Bailo, president and chief executive of the Center for Automotive Research, said: "We need to be fair and look at all the data.
"But I don't think anybody is taking this lightly. By far safety is the first concern."
The incident occurred on the streets of Tempe, Arizona, where the local Mayor Mark Mitchell has revealed he supports Uber's efforts to develop self-driving vehicles.
However, he also thinks the firm is right to suspend the tests at this time.
He explained: "Our city leadership and Tempe Police will pursue any and all answers to what happened in order to ensure safety moving forward."
On the other hand, Consumer Watchdog - a lobby group that repeatedly warned of the risks of autonomous vehicles - has said that the fatality was a "tragedy we have been fighting years to prevent".
In a statement on Twitter, the group added: "We hope our calls for real regulation of driverless cars will be taken seriously going forward by Silicon Valley and the Trump Administration."
The ride-hailing firm is one of a number of world-renowned companies that has been trialing autonomous vehicles over recent years.
Uber - which started testing driverless cars in Pittsburgh in 2016 - has recently been testing the cutting-edge technology on the streets of San Francisco, Pittsburgh, Toronto and Phoenix, which is near to where the fatality occurred.