According to Defence Ministry spokesman Muhammad Zahir Azimi on Tuesday, the device exploded as the soldiers were on their way from Asadabad to Nawabad in Kunar province.
The blast was caused by a remote-controlled bomb planted at the roadside and happened around 12:00am local time, Azimi added.
The attack comes as the commander of US forces in the country said both Taliban and Usama bin Ladin's al-Qaida network are renewing efforts to strengthen their positions.
Lieutenant-General David Barno said the US believed both bin Ladin and fugitive Taliban leader Mulla Umar were probably still in the region, possibly on the rugged border between Afghanistan and Pakistan.
"They're still providing financing, with guidance, training, support and selected individuals that help lead and motivate the operations here in Afghanistan," he said.
Barno, who leads a force of around 18,000 US troops in Afghanistan, added that al-Qaida members were "located in tribal areas, down there in border areas, probably on both sides of the border" with Pakistan.
As spring comes to Afghanistan, Barno added the movement would likely step up attacks, particularly along the Afghan-Pakistani border posts.
On Monday a bomb blast in eastern Kabul injured a Canadian man travelling in a diplomatic car and three other people. Police have arrested a suspect.
Unknown assailants also launched two rockets at the main US base in Afghanistan at Bagram, north of Kabul, on Monday but they caused no damage or casualties.