A spokesman for the governor of Helmand province said Thursday's attack took place in the provincial capital, Lashkar Gah.
Officials say the bomber hit a convoy of armored vehicles passing near the education department building.
A child was among those killed in the attack. Officials says some 31 others were wounded, including three foreigners: two men and a woman.
At least 17 civilian cars were damaged, some bursting into flames.
NATO has declined to comment on the attack.
There was no immediate claim of responsibility for the bombing, but Afghan President Hamid Karzai blamed the "enemy" of the Afghan people.
Mr. Karzai, who is in Italy, condemned the attack as inhuman and un-Islamic.
NATO transferred security control of Lashkar Gah to Afghan forces last year.
The Afghan president and NATO also condemned Wednesday's rocket attack in the eastern Afghan province of Kapisa that killed a woman and a child.
Also Wednesday, the Danish army said an Afghan baby was accidentally killed and the parents wounded when troops destroyed a roadside bomb in Helmand.
The Danish army said soldiers normally establish a security zone around the blast site and it was unclear how three civilians were hit by shrapnel. The case is being investigated.
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