Officials said that militants fired three rockets, which landed in Ghalla Mandi (Grain Market), a private school in Garhi Atta Khan and Mohalla Sikander Khan Shaheed areas of Kohat city on Tuesday.
Two policemen, a woman and a child were wounded in the attacks, a Press TV correspondent reported.
Militants fired four rockets in Hangu city. They also fired rockets at Kalya, headquarter of Orakzai Agency. However, no human loss was reported in both attacks.
Pakistani security forces targeted militant hideouts in Derra Adamkhel following the raids.
On day of Ashura, Shia Muslims across the globe are holding mourning rituals in commemoration of the martyrdom anniversary of the third Shia Imam, Imam Hussein (PBUH).
The event is one of the most important occasions on the Shia calendar.