The apparent target of the attack was an Afghan militia commander who was tribal elder named Haji Khan Jan and at least 10 others were among the dead.
Suicide blast happened in the eastern province of Kunar near the Pakistan border.
Provincial Governor Wahidullah Kalimzai said the bomber rode up on a motorcycle to the entrance of the government compound in the town of Asadabad and blew himself up.
"A suicide bomber detonated his explosives attached to his body in front of the provincial government headquarters. As a result of the blast 11 of our innocent people including children were martyred and 40 others are wounded," said Kalimzai.
There was no immediate claim of responsibility but Haji Khan Jan was closely involved in a number of operations against the Taliban in his district.
Several provincial officials in Kunar blamed Taliban insurgents because of Jan's vocal opposition to the group.