Officials said the pre-dawn bombing ignited a fire that burned the tankers, which had been carrying supplies to coalition forces and had been parked overnight in the Samangan province in northern Afghanistan, the BBC said.
Provincial security chief Gen. Khalilullah Andarabi said two drivers were injured in the incident, which he said occurred about 3 a.m., Khaama Press reported.
Officials said the attack was the first of its kind in northern Afghanistan.
The BBC reported an intelligence official said a bomb had been attached beneath one of the trucks, which were parked close to one another.
"Since it was early in the morning, there were not a lot of people around. Otherwise, it could have caused a lot more casualties,'' the official told the BBC.
The Taliban claimed responsibility for the attack in a statement.
NATO has been relying heavily on supplies shipped over land from Central Asia since November when Pakistan banned NATO convoys after U.S. airstrikes killed 24 Pakistani soldiers on the Afghan border.
Pakistan lifted the ban this month but NATO supply traffic still hasn't returned to normal.
Notable deaths of 2014 [PHOTOS]