"We are not sure whether it is a suicide blast," Salahuddin Kundi, a police officer, said.
The attack occurred amid an ongoing military offensive in a nearby tribal region that has left hundreds dead.
More deaths in Bajur
At least five soldiers and 13 suspected rebels were killed in clashes which continued for several hours, in Bajur, a Pakistani tribal region bordering Afghanistan, Mohammad Jameel, an administration official, said.
On Tuesday, police said security forces backed by helicopter gunships and artillery targeted rebels in the area, killing 11 suspected rebel fighters and five civilians over a 24-hour period, he said.
The fighting occurred when dozens of pro-Taliban rebels attacked a paramilitary post in Nawagai, 25km west of Khar, the main town in the Bajaur tribal district.
According to official figures released last week, the Bajur operation has killed nearly 500 people and displaced more than 200,000.
The country's tribal regions along the Afghan border in particular are considered safe havens for Taliban and al-Qaeda linked rebel groups, many of whom are believed to be involved in attacks on US and Nato forces in Afghanistan.