Rival group suspected
The Ansar-ul-Islam fighters operate in Khyber tribal district near the border with Afghanistan.
Ghayyur said police suspect that Lashkar-e-Islam, a rival group, could be behind the bombing.
Up to 10 kilogrammes of explosives were used in the device, which was planted under the car, said Shafqat Malik, a bomb disposal official.
Sahibzada Anis, the head of district administration, said that the bombing took place on a road that was normally busy but there were fewer people out due to the onset of the holy Muslim month of Ramadan.
The government last year launched a major operation against groups in Khyber which sent their leaders moving into the mountains bordering Afghanistan, after the militants threatened to take over Peshawar.