About 20 people were travelling in the vehicle.
They were returning home to celebrate the upcoming Eid-ul-Fitr festival.
The vehicle hit a landmine and exploded, killing 10 people, witnesses said.
The condition of three of the injured was described by local officials as critical.
No group claimed responsibility for the attack.
Hundreds of people have died due to sectarian violence and militant attacks in Kurram Agency over the past three years. The region has been rocked by clashes between rival Shia and Sunni tribesmen.