The truck was travelling near the city of Dayton when the driver lost control and hit a roadside barrier.
The driver escaped unhurt, but a female passenger, his fiancee, was injured.
Police said up to 400 piglets were killed but at least 1,500 were rescued, and it is unlikely that all the escapees will be rounded up.
The surviving pigs were taken to a nearby agricultural fairground, where they are now being cared for.
Emergency crews rescued them by forming a human chain and lifting them to safety.
Dean Fox, a fire chief in Xenia in Ohio, spoke to the Dayton Daily News about the animals that had escaped.
"Probably we'll never get a hold of them," he said. "We'll try as hard as we can, but we probably won't retrieve them all."
A truck carrying 2,200 piglets has overturned in the US state of Ohio, lead to hundreds of the animals escaping into nearby woods.