Bannu District Police Officer (DPO) Yasir Afridi confirmed the incident and the casualty figures to Dawn News.
He said security forces and law enforcement agencies rushed to the area immediately after the blasts, collected evidence, and launched an investigation.
In a statement, police said the two vehicles were targeted in "remote-controlled blasts" in the Phang Musa Khel area, describing the attacks as a "cowardly act of terrorism", according to Dawn.
Police said the first explosion targeted a private Datsun vehicle carrying passengers. As the injured were being transported to a hospital, a second blast occurred.
Eyewitnesses told Dawn News that the second explosion took place nearly a kilometre away from the site of the first attack.
Authorities have cordoned off the area and launched a search operation to trace those responsible.
Bannu has witnessed growing security challenges in recent months, with civilians and security personnel frequently coming under attack amid a broader surge in militant violence across the region.