The building on University Road, which houses the office of the Criminal Investigation Department, was destroyed by the powerful blast.
Senior Khyber-Pakhtunkhwa Minister Bashir Bilour confirmed that the attack was carried out by a suicide car bomber.
"About 300 kg of explosives was used in the attack. The engine of the bomber's car landed 350 feet away and his body was blown to bits. Only one finger of the bomber has been found," Bilour told reporters after visiting the site of the attack.
Officials said two policemen were killed by the powerful blast, which occurred at 4.45 am local time. Eighteen people, including a child, were injured and were taken to two nearby hospitals. Doctors described the condition of the two injured policemen as serious.
Police and rescue workers said several policemen could be buried in the rubble of the building, whose walls and ceiling collapsed after the blast.
Army soldiers and policemen cordoned off the area and sealed the University Road. Footage on television channels showed heavy machinery being used to remove the debris of the police building.
No group claimed responsibility for the attack, which came barely three days after a group of Taliban fighters sneaked into a naval airbase in the southern port city of Karachi and killed 10 security personnel and destroyed two maritime surveillance aircraft.