Police at the scene said that as many as six Afghan civilians were also injured in the bombing.
Taliban members carried out the attack, Zabihullah Mujahid, a spokesman for the group, said.
The bombing is only the latest attack carried out by Taliban members in the nation's capital.
Late on Wednesday, a member of Afghanistan's parliament who was prime minister for a few weeks in 1992, was assassinated outside his home by unknown men.
Abdul Sabur Farid Kuhestani, aged in his mid-fifties, was shot dead in an ambush, Ali Shah Paktiawal, the city's criminal investigation chief, said.