Two soldiers in the car were killed on the spot and another was injured in the attack. Three children playing on the side of the road were seriously injured. The statement said that all the injured were taken to the hospital by helicopter but no one survived.
No group has claimed responsibility for the attack. The military says security forces and intelligence officials have been searching the area for handlers of the bombers.
The area has been a safe haven for local and foreign militants for years. The military launched a major offensive in 2014 after militants attacked an army-run school in Peshawar, killing more than 150 people, most of them schoolchildren.
Also on Sunday, police officer Ejaz Khan said gunmen on motorcycles opened fire on two members of the minority Sikh community at a market in the Peshawar suburb of Sarband.
Khan said Ranjit Singh, 38, and Kanwal Jeet Singh were shot more than once while setting up their spice shop at Batta Tal Bazaar on Sunday. The assailants fled the scene.
Liability was not immediately accepted. Police were investigating but Khan said the two Sikhs appeared to have been targeted for their ethnic reasons. Shikhara is a small minority in northwestern Khyber Pakhtunkhwa province and has been targeted by militants in the past.
Meanwhile, Pakistani health authorities have registered the third case of polio of the year in Miranshah, North Waziristan. The country’s anti-polio program coordinator and spokesman. Mohammad Shahzad said a deadly virus had been detected in a one-year-old boy. There was only one case in the country last year.