A spokeswoman for Skelton, Lara Battles, confirmed that a vehicle accident was reported and said it was her understanding that Skelton was OK.
"All indications that we've received are that everybody is doing fine," Battles said but added that she could not comment further on the accident or the trip.
Marshall, a Georgia Democrat, said he was not hurt.
The congressional delegation was riding in a box-like vehicle that troops called the "ice cream truck" that streaked through the middle of the road to deter oncoming motorists, Marshall said.
But shortly after dark, an oncoming truck refused to yield.
"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 told The Macon (Ga.) Telegraph by phone from Baghdad
Marshall said as the vehicle toppled over, he held onto Skelton, who has limited use of his arms due to a bout with childhood polio.
The embassy said the driver's quick reaction "probably averted disaster."
"Everybody sort of fell over to the side. There's no cushion to it. It's all solid metal with bolts sticking out," Marshall told the newspaper. "I feel like a fool. I didn't put my seat belt on."
The accident reminded Marshall of his first trip to Iraq with Skelton, when Marshall voiced concerns on the dangers of the high-speed driving strategy aimed at getting dignitaries safely through treacherous territory.
"It's so odd to me that I said, 'Shoot, this is more dangerous than the terrorists,' and dang if we don't flip over," Marshall said.
The delegation had traveled to Afghanistan for Thanksgiving with the troops and then on to Baghdad to meet with troops. It was Marshall's sixth visit to the war zone.