Another senior police officer confirmed the attack, adding that around 200 kilogrammes of explosives were used.
The attack comes just a day after two suicide bombers dressed in burqa struck a crowd of displaced people collecting aid handouts, killing at least 41 and wounding more than 60 at a nearby camp.
The bombers struck minutes apart on Saturday in the Kacha Pukha camp on the outskirts of Kohat.
The camp is meant for people for people fleeing Taliban violence and Pakistani army operations in the region.
Al Jazeera's Kamal Hyder, reporting from the capital, Islamabad, said most of the victims were the displaced people from the Orakzai agency where the military has launched an offensive recently.
The Pakistani military stepped up an offensive against Taliban-allied fighters in Orakzai late last month.
The UN said earlier this month that the deteriorating security situation in Orakzai and neighbouring Kurram district has forced 200,000 civilians to flee since November last year.