The simultaneous explosions occurred overnight in the town of Reghaia, 30km east of the capital Algiers, and the eastern Algiers suburb of Dergana.
They were the first large bomb blasts around Algiers since the summer of 2003, when violence that is believed to have claimed between 150,000 and 200,000 lives since 1992 began to subside.
The explosion in Reghaia burned parts of the two-storey building, gouged a hole in the pavement at least one metre deep, shattered windows for several blocks and hurled parts of the truck more than 100 metres from the scene.
At least eighteen cars were destroyed.
Local residents said the Reghaia attack began when gunmen firing automatic weapons threw a grenade at the entrance to the police station. At the same time, accomplices parked a truck rigged with explosives at the side of the building and then made their getaway in a car before setting off the bomb.
A security source said the blast in Dergana was minor and that most if not all the casualties had occurred in Reghaia.
Another source told Reuters news agency that the vehicle in Reghaia appeared to have been a rubbish truck stuffed with 60kg of explosives. The vehicle used in the Dergana attack was probably a car, he added.
Islamic groups began armed action in 1992 after the government scrapped a parliamentary election that the Islamic Salvation Front (FIS) was set to win.
President Abdelaziz Bouteflika has pledged to crush groups which refused to surrender during a six-month amnesty which expired on August 31.
The FIS remains banned and a state of emergency first imposed in 1992 is still in force.
Reghaia is in a region where fighters from the Salafist Group for Preaching and Combat, which refused to take part in the amnesty, are reported to be hiding out.
The amnesty would have meant that charges against members of armed groups who did not participate in massacres, bombings in public areas or rapes would have been dropped.
Members of the security services who were linked to disappearances and violence would also have been given immunity under the plan.