The oil tankers were parked at the Torkham border terminal when they were targeted with timed explosive devices.
At least 10 tankers were destroyed by the blaze and another exploded while the fire was being doused, officials said.
Eight of the dead belonged to the same family. Six persons were killed instantly while 10 more succumbed to their injuries in hospital.
Tankers ferrying fuel for NATO forces in Afghanistan travel from the port city of Karachi to the northwestern border town of Landi Kotal through insurgency-hit areas where they are frequently attacked.