The attack came as Afghan troops patrolled a remote mountain pass on Monday, according to General Murad Ali of the Afghan National Army.
In a separate attack, a Nato convoy in the capital, Kabul, was attacked by a bomber. Three soldiers and three civilians were wounded.
The bomber ran in front of the military convoy, said Ali Shah Paktiawal, a senior police official.
Sayid Rahman, a witness to the scene, said: “I saw an American four-wheel drive entering Kabul and suddenly a guy who was standing next to a pump station ran towards the vehicle and detonated himself.”
Three Nato-led troops received minor injuries, said Major Luke Knittig, a military spokesman. He would not disclose the nationalities of the soldiers. Three civilians were also injured.
Police detained the driver of the car that dropped the bomber off minutes before the blast, Nato said.
The attack came two days after another suicide bomber killed 12 people and wounded more than 40 outside Afghanistan‘s interior ministry.
On Sunday in the southern province of Helmand, ambushes and clashes left 10 people dead, including five civilians, according to Ghulam Muhiddin, the governor’s spokesman.
The civilians were killed when their vehicle hit a mine on a road usually used by Nato and Afghan forces in the Musa Qala district.
Muhiddin also said a suspected Taliban member on a motorbike had killed two policemen and wounded two others in Gereshk district.
While in the Nawzad district, Nato-led troops and Afghan forces had been fighting insurgents, leaving three militants dead and two wounded, he said.
A separate two-hour clash between insurgents and police in Paktia province on Sunday also killed two Taliban fighters and wounded four.
Southern Afghanistan has been rocked by the worst outbreak of fighting since the Taliban government was overthrown by the US-led invasion in 2001.
Taliban members have increasingly used human bombers and roadside bombs in their attacks.