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. At least another 40 people were also wounded.
"Most of victims were civilians and children who were either passing by or playing in the park," he said, Reuters reported.
There was no immediate claim of responsibility but the apparent target of the attack, a tribal elder and militia commander named Haji Khan Jan, was among the dead.
He had been closely involved in a number of operations against the Taliban in his district last year.