According to Ghulam Muheddin, the provincial governor's spokesman, the bomber, on foot, let off his explosives opposite a police station in Lashkar Gah, the capital of the southern Helmand province.
Hanif Khan, a local hospital official, said that of the 47 people wounded, 15 were children and six were critically injured.
Shattered glass from shop windows, human parts and blood-soaked turbans were scattered at the site, one witness said.
Among the dead were the owner of the market, a former Lashkar Gah police chief, his son, and a nephew.
Insurgents usually target Nato-led and Afghan soldiers in southern Afghanistan, although civilians are sometimes the victims.
A human bomber apparently targeting Canadian soldiers earlier this month in Panjwayi district of the neighbouring Kandahar province killed 21 civilians and wounded 13 others.
Afghanistan is enduring its bloodiest phase since US-led forces invaded Afghanistan and overthrew the Taliban government in late 2001.