A total of 41 people, most of them civilians, were injured when the bomber targeted the local district administration compound in the town of Paghman, said a police spokesman, Ebadullah Karimi.
"At around 10:30 this morning local time, a suicide attacker detonated his explosive-packed car next to the Paghman district headquarters. Two police officers and two civilians have been killed, a further 41 have been injured," Karimi said, according to AFP.
A senior police officer was among the dead, Karimi added. Paghman is 20 kilometres (12 miles) west of Kabul.
The account was confirmed by the interior ministry deputy spokesman Najib Danish.
The Taliban, who have been waging a bloody insurgency since their regime was toppled in late 2001, claimed responsibility for the attack.
Afghanistan has witnessed escalating violence since the insurgents launched their spring offensive in April.
Nearly 1,600 civilians were killed and 3,329 injured in the first half of this year, according to UN figures.