The first blast occurred near a girls' school located in the congested Gardan Ali Bazar of Bannu district, which borders North Waziristan tribal region.
The explosive device, planted in a culvert near the primary school, exploded with a loud bang. Twelve students and six passers-by were injured, police said.
The injured were out of danger, the officials said. They were taken to a nearby hospital.
The bomb exploded as students were leaving school after the end of classes. The nearby bazar was packed with shoppers, many of them women.
Police said the attack was carried out on Peshawar-Torkham Road. The injured were taken to a nearby hospital.
No group claimed responsibility for both attacks though the Taliban frequently attack girls' schools.