The blast occurred on Monday after a bomber blew his explosives up in the line of people waiting to enter a local police office in the Dehmazang area of Kabul.
Rescue personnel rushed to the scene following the blast and transported the injured to a nearby hospital.
No group or individual has so far claimed responsibility for the attack, but the government blamed the Taliban for the raid.
Kabul saw a series of bomb attacks last month, including one that killed seven journalists from a private television station as the Taliban intensified its campaign of terror.
Afghanistan is gripped by insecurity 14 years after the United States and its allies attacked the country as part of Washington’s so-called war on terror. The 2001 attack overthrew the Taliban, but many areas across Afghanistan still face violence and insecurity.