Rep. Tim Murphy, a Republican, was airlifted to a military hospital in Germany for an MRI on his neck, and Rep. Ike Skelton, a Democrat, was sent to a Baghdad hospital, said Rep. Jim Marshall.
Marshall, a Georgia Democrat, was in the vehicle but was not hurt.
The politicians were riding on Sunday in a box-like vehicle in a convoy. The convoy was taking up the middle of the road, a common practice used by the military to deter oncoming motorists. Shortly after dark, an oncoming truck refused to yield, Marshall said.
"Then all of a sudden brakes get slammed on. Then we hit something and go off the side of the road and tip over," Marshall added.
He said that as the vehicle toppled over, he held onto Skelton, who has limited use of his arms due to childhood polio.
The delegation had travelled to Afghanistan for Thanksgiving with the US troops and then on to Baghdad to meet the troops there.
Calls to Skelton and Murphy on Sunday were not immediately returned; but Marshall's spokesman Doug Moore said both suffered minor injuries. The US Embassy in Baghdad confirmed the accident but declined to release further information.