The vehicle was travelling in Pakistan's Khyber region on Saturday when it was struck about 15km west of the city of Peshawar.
"Seven paramilitary soldiers were killed and 11 were wounded in the remote-control bomb attack," Shafirullah Khan, the chief administrative official of Khyber tribal district, told the AFP news agency.
Khyber is on the main supply route through Pakistan to Afghanistan, where international military forces are fighting the Taliban.
The bomb blast came as Pakistan's military continued its offensive against Taliban fighters in South Waziristan, in the country's northwest.
Pakistani fighter jets bombed three suspected Taliban positions in the Orkazai tribal region on Saturday, the Associated Press news agency reported.
At least eight fighters were killed and several others wounded, the news agency cited intelligence officials as saying.
The military launched the offensive two weeks ago, pitting about 30,000 Pakistani troops against an estimated 10 to 12,000 members of the Tehreek-e-Taliban Pakistan (TTP).
Asif Ali Zardari, Pakistan's president, has said security forces will not stop until they have defeated the fighters.
"There [is] no turning back ... until the complete elimination of the militants," a statement from his office said on Friday.
His pledge follows comments from Hillary Clinton, the US secretary of state, who suggested on Thursday that Pakistani officials could do more to find and fight al-Qaeda and the Taliban.
She said al-Qaeda had enjoyed a "safe haven" in Pakistan since 2002 and said that some Pakistani officials might know where the group's leaders are hiding.
"I find it hard to believe that nobody in your government knows where they are and couldn't get them if they really wanted to," Clinton said to a group of newspaper editors in the city of Lahore during a three-day visit to the country.
Source: Al Jazeera (English)