The convoy came under fire on Saturday near Deh Rawood in Uruzgan province, governor Jan Muhammad Khan said.
He had no details of who carried out the attack, or on the condition of the injured soldiers.
The US military had no immediate comment.
Khan said US troops returned to the area on Sunday, arresting three relatives of Haji Ghulam Nabi, a tribal leader who Khan said had close ties to the former Taliban government. Nabi had gotten away, he said.
Deh Rawood, where the US military has a base, is considered a Taliban stronghold and shootings and rocket attacks near the base occur regularly.
An Afghan soldier was killed in the area on 2 December in a gunbattle between US-led forces and guerrillas. A US special forces soldier died on 30 October about 55 kilometres to the west.
Taliban guerrillas have also been blamed for kidnapping a local driver from the Shelter for Life charity in Afghanistan.
Afghan security official Qudrat Allah said the kidnapping occurred on Sunday outside Qalat, the capital of the southern province of Zabul where Taliban guerrillas have been active in recent months.
Taliban official Haji Hakim Latifi confirmed the Taliban were behind the kidnapping, but did not issue a demand or ultimatum.
|Afghanistan's power brokers seen|
here at the latest Loya Jirga have
failed to quell the Taliban
A Shelter for Life official said two trucks in a three-vehicle convoy had reached Kandahar safely, but there was still no word from the third driver in an off-road vehicle.
"Obviously we are a little bit worried," he said, adding the truck drivers had yet to give their account of the incident.
Taliban to be freed
Meanwhile, a powerful Afghan commander has decided to free hundreds of former Taliban fighters held in a prison in the northern town of Shiberghan.
The move by Uzbek General Abd al-Rashid Dostum follows appeals by relatives of the captives at an assembly which adopted a new constitution on Sunday after nearly 25 years of occupation and civil war.
The fighters have been held in the prison since it fell to US-led forces in late 2001.
At the height of the US-led war that led to defeat of the Taliban regime, Dostum's forces captured hundreds of Taliban and al-Qaida fighters during battles in the north.
Dostum's loyalists are accused of allowing hundreds of Taliban fighters to suffocate while being transported to the prison in metal containers. Dostum denies the charge, but says many may have died from wounds sustained during fighting.
He has already released hundreds of Taliban fighters from his jail, including many Pakistanis.
Faiz Allah Zaki, Dostum's spokesman, said on Monday about 450 Taliban fighters and a similar number of Pakistani
prisoners were being held at the jail.
Drugs lab destroyed
In another incident, the US military said an airstrike destroyed a drugs laboratory in the far north of the country.
|Afghan policemen and soldiers are|
favoured Taliban targets
Several people were detained by US and Afghan troops in the Friday raid on the lab, about 90 kilometres northeast of Kunduz, a spokesman said.
An A-10 ground attack aircraft was called in to destroy the facility, which contained about two tons of drugs and equipment, Lt Col Bryan Hilferty said.
Cultivation of opium poppies, the raw material for heroin, is booming in the north of Afghanistan after the ousting of the Taliban. The country already supplies nearly three-quarters of the world's opium.
About 11,700 soldiers from the United States and other countries remain in Afghanistan to fight suspected Taliban and al-Qaida members. But reports of raids on drug facilities or smugglers are rare.