Three other family members were wounded in the incident which took place near Baquba at around 6.30am (0330 GMT) as they were returning from a funeral, police and hospital sources said.
Ahmad Kamil al-Sawamara, a 22-year-old student who was driving the car but escaped serious injury, said he suddenly saw US military vehicles just ahead of him.
"The soldiers started shooting at us from all over. I slowed down and pulled off the road, but they continued firing," he told reporters.
"I saw my family killed, one after the other, and then the car caught fire. I dragged their bodies out."
Two men and three children, aged one, two and three, were killed, and two women and a child were wounded, Iraqi police said.
A US military spokesman confirmed the shooting, but put the toll at three dead and two wounded.
US troops had set up a makeshift roadblock to allow some military vehicles to turn off a highway into a base when the civilian car approached, said Major Steven Warren.
"I saw my family killed, one after the other, and then the car caught fire. I dragged their bodies out"
Ahmad Kamil al-Sawamara, 22
"The Iraqi car wouldn't slow down and warning shots were fired," he said.
The car failed to stop and came under machine-gun fire, Warren added. Medics travelling with the patrol immediately gave first aid after the incident.
US forces, who regularly face attack by bombers trying to ram their vehicles before setting off their explosives, have repeatedly been involved in shooting incidents in which civilians have been killed by mistake.
US patrols carry warning signs telling people to keep at a distance and drive down the middle of highways forcing oncoming traffic off the road.