The civilians were killed in an explosion in Spin Boldak district of Kandahar province, said district government chief Abdul Ghani.
The bomb was attached to a motorcycle parked in the main market, he said. The blast injured more than 10 people.
The NATO service member was killed in a separate explosion. The international military coalition did not provide further details or the nationality of the dead service member.
The convoy attack started in the early morning when a group of gunmen rushed on the trucks in Behsud district of Nangarhar province — the same area on the edge of Jalalabad city where a group of would-be suicide bombers tried to storm a NATO base on Saturday, said Ahmad Zia Abdulzai, a spokesman for the provincial government.
The drivers of the trucks quickly fled and the insurgents set 12 tankers ablaze, said Abdulzai.
Firefighters worked to quell the flames throughout the morning, as police secured the area. No one was killed in the attack, Abdulzai said.