It happened at 5:30 a.m. near Route 299 in Middletown.
Images from Chopper 6 HD showed the truck on its side and a load of what appeared to be sand spread on the road and in the median.
Delaware State Police say the truck driver swerved to avoid hitting a car that pulled onto the roadway from the right shoulder.
Police say 25-year-old Joshua Thompson of Smyrna, the driver of the dump truck, was treated at a hospital for minor injuries. The driver of the car, 75-year-old Ted Schaum of Viola, was not injured.
Schaum was cited in the crash.
Part of Route 1 was shut down following the crash. All lanes were back open by 9:30 a.m.