The dead included a number of street children, the Los Angeles Times reported.
The attacker, on a motorcycle, blew himself up near the entrance of Camp Eggers, which houses 2,500 members of the NATO-led forces.
No one on the base was injured.
The blast occurred in a market place in the Shash Darak area of the city, Khaama Press reported.
There were conflicting reports on the number of dead and injured.
Unofficial accounts said at least five Afghan children were killed or injured. A spokesman for the interior ministry said at least four people were killed or four others injured.
The Taliban claimed responsibility.
Afghanistan is marking the 11th anniversary of the death of Ahmadshah Massoud, a national hero who fought against the Russian invasion and resisted the Taliban.
Notable deaths of 2014 [PHOTOS]