Waymo - a company spun out of Google - filed a lawsuit in February claiming former employee Andrew Levandowski had stolen 14,000 documents relating to LiDAR, a core technology used to guide autonomous vehicles.
Mr Levandowski went on to co-found Otto, a self-driving truck company acquired by Uber for $660m last year.
Waymo requested a judge grant an injunction on the use of the disputed technology, which could take Uber’s self-driving fleet - currently being tested in a few locations in the US - off the roads.