Mokhis Afghan, spokesman for the provincial governor of Paktika, told the Associated Press that the attack happened in the late afternoon as a large crowd gathered to watch a volleyball tournament in Yahyakhail district.
Another spokesman, Mukhles Afghan, told Reuters that more than 50 people were wounded in the blast.
The bomber is said to have walked into the dense crowd and detonated his explosive vest.
Most of the casualties are said to be civilians.
No group has yet claimed responsibility for the attack, but the Taliban has previously carried out bombings in Paktika province.
In a statement, the head of the International Olympic Commitee, Thomas Bach, condemned the attack as "cowardly."
"It is an attack on sport itself and on the positive values it can bring to help build strong communities and foster peace and reconciliation around the world," Bach said.
Details remain scarce because of the remoteness of the location.