There was no immediate claim of responsibility for the bomb in the northwestern city, near the border with Afghanistan, which has long been plagued by Islamist violence.
Though militant violence in the city, and in Pakistan in general, has fallen over recent years, there has been an increase in attacks on the security forces this year in Khyber Pakhtunkhwa province, of which Peshawar is capital.
Some of the attacks have been claimed by the Pakistani Taliban.