The vehicle was on a routine patrol on the outskirts of the town of Dera Ismail Khan on Sunday when the bomb, apparently planted in a dusty road, exploded as it passed over it.
Daar Ali Khattak, the district police officer, speaking to reporters, said: "It was a remote-controlled bomb,"
Khattak said a passerby was among the dead, and hospital officials said five people were wounded including two women.
No one claimed responsibility for the attack but Aftab Ahmed Khan Sherpao, the interior minister, said Islamist attackers were probably behind the blast.
Dera Ismail Khan is close to the troubled Waziristan tribal region where security forces have been battling with al-Qaeda-linked fighters and their local supporters over the past two years.
"It appears to be the spill over of what is going on in Waziristan," Sherpao told Reuters.
Nearly 200 pro-Taliban fighters have been killed in clashes with the security forces in the North Waziristan tribal region this month.
Many al-Qaeda fighters and their Taliban supporters fled to the semi-autonomous tribal belt after US and Afghan opposition forces toppled the Taliban in Afghanistan in 2001.
Pakistani security forces have been trying to clear foreign fighters from the area and subdue their Pakistani allies since 2004.
"It appears to be the spill over of what is going on in Waziristan"
Aftab Ahmed Khan Sherpao,
Pakistan Interior Minister
Khattak said security had been reinforced in Dera Ismail Khan and nearby Tank town over concerns of attacks.
"We consider these towns as hot targets of the militants," he said.
Police in Tank last week issued a warning to local authorities that fighters could target government offices, buildings and vehicles in retaliation for the military's crackdown against them in the tribal areas.
Pakistan's tribal belt and areas on the Afghan side of the long border are dominated by ethnic Pashtuns.
Many tribesmen sympathise with the Taliban, also Pashtuns, and al-Qaeda leader Osama bin Laden and his deputy Ayman al-Zawahri are believed to be hiding in the region.
Afghan officials have long complained that Islamist attackers use Pakistani territory as a springboard for launching attacks inside Afghanistan.
Pakistan, an ally in the US-led war on terrorism, says it is doing all it can to stem the cross-border movement of the fighters, and has urged Afghan authorities to do more on their side of the porous border.