"We have received two dead bodies and 12 injured, including one woman," Zafar Iqbal, a doctor at the hospital, was quoted by the AFP news agency as saying.
The dead included the officer and an accountant who worked for the press club, authorities said.
A woman who was at the site died of cardiac arrest caused by the shock of the bombing, Sahib Gul, another doctor, said.
The force of the explosion blew out the windows in the red brick press club building, damaging the guard hut outside and nearby vehicles.
Peshawar has been a frequent target for bomb blasts.
Pakistan has seen a series of attacks across the country in recent months, attributed to fighters retaliating to the army's offensive against the Taliban in the South Waziristan tribal region.