The incident came during operations in the vicinity of Gardez, in Paktya Province. U.S. Central Command did not name the soldier.
In another incident, coalition troops detained a man near Kandahar when he was spotted carrying the same kind of rockets frequently fired at U.S. bases.
The military believes the insurgents are a mix of holdouts from the former Taliban regime, fugitive members of the al Qaeda terrorist network and loyalists of a former prime minister.
There are 11,500 soldiers from 23 countries still in Afghanistan, and roughly 9,000 Americans. In early May, Defense Secretary Donald Rumsfeld declared the end of major combat there.
Earlier this month, a car packed with explosives pulled up to a bus carrying German peacekeepers in Kabul and detonated, killing four and wounding more than two dozen in the first fatal attack on the international force.
The bus was taking 33 German peacekeepers to Kabul's international airport to return home - some on leave, some after completing their mission in Afghanistan - when the attack took place, said a spokeswoman for International Security Assistance Force, or ISAF.
Afghanistan has seen an upswing in attacks - thought to be by Taliban fighters - against American troops, particularly in the south and east.
Since the United States broadened its anti-terrorism campaign to include Iraq, there has been a surge in violence against Westerners in the Islamic world. A May 12 attack on housing complexes in Saudi Arabia killed at least 23 people, bombings in Morocco killed 31 victims, and there have been continued guerrilla assaults on U.S. troops in Iraq.
Before the explosion that killed the Germans, 15 peacekeepers had died on duty in Afghanistan, all in accidents. In addition, 62 Spanish peacekeepers were killed in May when their plane crashed in Turkey as they were returning home after a four-month tour of duty in Afghanistan.
On May 15, two Norwegian peacekeeping troops were shot and wounded by a renegade Afghan soldier as they were traveling on a road north of Kabul. Two days earlier, a British soldier was slightly wounded when an Afghan man threw a grenade at a peacekeeping base.
In March, ISAF's headquarters in downtown Kabul was hit by a rocket, but no damage or casualties occurred. Also in March, an explosive device set off by remote control in Kabul wounded one Dutch peacekeeper and killed an Afghan translator.
Some 5,000 peacekeepers are in Kabul. Germany and the Netherlands currently command the force but are to hand over control to NATO Aug. 11. At about that time, German and Dutch forces are to return home and be replaced by about 1,800 Canadian troops.