The attack in the town of Urgun in Paktika province was the deadliest in months in Afghanistan, underscoring the country's instability as foreign troops prepare to leave by the end of the year.
Gen Mohammad Zahir Azimi, the Defence Ministry spokesman, said the bomber detonated his explosives-laden vehicle as he drove by the crowded market in the remote town in Urgun district, close to the border with Pakistan.
The military was providing helicopters and ambulances to transport the victims to the provincial capital, Sharan, and, so far, 42 wounded have been moved to hospitals there, Mr Azimi added.
The explosion also destroyed more than 20 shops and dozens of vehicles, he said.
No one immediately claimed responsibility for the attack but the Taliban sent a statement to media denying their insurgent group was involved in the Paktika bombing and saying they "strongly condemn attacks on local people."
Many of the victims were buried under the rubble, said Mohammad Reza Kharoti, the administrative chief of Urgun district.
"It was a very brutal suicide attack against poor civilians," he said. "There was no military base nearby."
The bombing was also the first major attack since a weekend deal between the two Afghan presidential contenders brokered by US secretary of state John Kerry averted a dangerous rift in the country's troubled democracy.
One of the two, former finance minister Ashraf Ghani Ahmadzai, told The Associated Press on Monday that he would meet his rival, former foreign minister Abdullah Abdullah, on Tuesday to begin working out the framework for the next government, with participation from both camps and all communities in the country.