The attack on the military convoy occurred in Khan Azad some 20 kilometers south of Baghdad.
Two soldiers were evacuated to a military hospital.
One was pronounced dead on arrival.
The incident is the latest in a series of almost daily attacks and ambushes against U.S. troops in Iraq.
On Saturday two American soldiers were injured when their vehicle ran over a landmine near the town of Hit some 150 kilometers from Baghdad.
In the same area an explosion late Saturday set a major oil pipeline on fire.
Local officials are calling it sabotage but the military says it is still investigating the incident.
In another development Iraq resumed oil exports Sunday for the first time in three months.
Iraqi oil was being loaded onto a Turkish tanker at the Turkish port of Ceyhan.
Oil exports were halted in March because of the U.S.-led war to oust the government of Saddam Hussein.