According to a dispatcher in Tooele County, no one was injured in the incident.
A Utah Highway Patrol representative said the truck was on its way to Energy Solutions, a company that processes low-level radioactive waste.
According to UHP, no one touched the trailer or the radioactive material inside.
The truck fire also sparked a small brush fire nearby. Both fires have been extinguished.
A tweet from Tooele County Emergency Management said the incident does not pose a threat to the public.
The cause of the truck fire is unknown.