Residents told an AFP reporter in Fallujah that Ahmed Latif, 32, whom they said was mentally disturbed, insulted the soldiers as they patrolled in the centre of the city, and then hurled a shoe at them.
The US military told AFP that a convoy in Fallujah had been attacked with a suspected grenade.
"Positive identification of the attacker was made, and US forces fired in self-defence wounding the attacker," the army said in a statement.
"Local Iraqi police secured the scene and transported the wounded attacker to a local hospital for medical care," it added.
Dr Ali Hatam of Fallujah hospital confirmed that Latif died of gunshot wounds.
The incident came a day after Iraqi journalist Muntazer al-Zaidi was freed after spending nine months in jail for throwing his shoes at former US president George W. Bush during a visit to Baghdad.