The vehicles were hit by a pre-dawn explosion which triggered a huge fire that engulfed them in flames, they say.
At the time, the trucks were parked overnight in Samangan province, as they headed from Uzbekistan towards NATO forces in the south.
Police said the fire caused by the bomb is still burning.
An intelligence official said the device was attached under one of the trucks, which were parked close together.
“Since it was early in the morning, there were not a lot of people around. Otherwise, it could have caused a lot more casualties,” said the official.
In a statement, the Taliban said they carried out the attack, which officials say is the first of its kind in northern Afghanistan.
The trucks were attacked in the same province where well-known Afghan politician Ahmad Khan Samangani was killed in a suicide attack on Saturday while attending his daughter’s wedding.
NATO has relied heavily on overland supplies from Central Asia since last November when Pakistan banned NATO convoys after US airstrikes killed 24 Pakistani soldiers on the Afghan border.
Although Pakistan lifted its blockade earlier this month, NATO traffic has yet to return to normal.
While attacks on NATO tankers have been commonplace in Pakistan in recent years, correspondents say such attacks in Afghanistan have been much less frequent.
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