According to local officials, two vehicles escorting the convoy were also destroyed in the ambush on Tuesday Press TV reported.
One person was killed in the attack and two others were injured, the officials said.
A spokesperson for the Taliban, however, claimed that at least six people had lost their lives.
Taliban militants have also destroyed hundreds of NATO tankers and trucks in Pakistan over the past year.
Pakistan recently blocked the border crossings used to transfer NATO supplies for US-led forces into landlocked Afghanistan.
Islamabad took the measure after a US-led airstrike killed 26 Pakistani soldiers on November 26.
Prior to the closure, the supplies would arrive by sea in Karachi, from where they would be carried in long, exposed convoys, through Khyber Pakhtunkhwa Province in northwestern Pakistan.
Using other routes, which largely pass through Russia and Central Asian states, has proven to be too costly, both politically and economically.
Source : Afghan Voice Agency (AVA), Kabul