The attack came as an all-Afghan peace conference, which includes the Taliban, was underway Sunday in Doha in an effort to end the country's relentless wars.
A provincial council member, Hasan Raza Yousafi, said the car bomb exploded nearby an intelligence department compound in Ghazni, the capital of the province of the same name. The dead included eight security personnel, he said.
Many of the wounded were students of a nearby high school, said the provincial health department chief, Zahir Shah Nekmal. He said most of the injured suffered cuts and abrasions from broken glass.
Taliban spokesman Zabihullah Mujahed claimed responsibility for the suicide attack saying the target was the intelligence service's compound in Ghazni. He said the bombing killed tens of intelligence employees. The Taliban often exaggerate such claims.
Meanwhile, U.S. Peace Envoy Zalmay Khalilzad hailed the intra-Afghan talks underway in Doha as a good first step toward substantive negotiations between Afghans on a framework for the country's future.
He said Washington's "aspiration" is to have that framework in place by Sept. 1 and ahead of the Afghan presidential election.
Khalilzad, who has been holding direct talks with the Taliban for the past six days also in Doha, told a press briefing on Saturday that included The Associated Press that the discussions were the most productive ever.
He will resume talks with the Taliban on Tuesday, he said.
Meanwhile in western Ghor province, a roadside mine killed Saturday seven children — the youngest was just 5 years old.
Abdul Hai Khateby, a spokesman for the provincial governor, said the Taliban planted the mine apparently to thwart a planned Afghan military offensive to retake nearby areas under the militants' control. The children were local shepherds who happened to be moving their herd along the road when the mine exploded, he said.
Associated Press writer Kathy Gannon in Kabul, Afghanistan, contributed to this report.