The incident occurred in the Ghakay area of Bajaur Agency, close to the border with Afghanistan.
The vehicle was on its way to Khar,
Syed Badshah, a doctor at the state-run hospital in Khar, said the body of a woman and 22 injured people had been brought to the facility.
The condition of three persons is critical, he said.
The Pakistan Army conducted a major offensive against the Taliban in Bajaur Agency last year.