Interior Ministry spokesman Sediq Sediqi told CNN only one of two suicide bombers detonated his explosives. The second was arrested.
The attack was in the northern province of Baghlan on the first day of the Muslim feast of sacrifice, Eid al-Adha, he said.
Sediqi told the broadcaster there was little doubt about who orchestrated the attack and its timing.
"Our preliminary investigation shows that this attack was carried out by the Taliban," Sediqi said. "We strongly condemn this terrorist act, on one of the holy days for Muslims."