The attack occurred in the Ghaziabad district of Kunar province, provincial governor Shujah-Ul Mulk Jalala told AFP.
The Taliban later issued a statement claiming responsibility.
The governor said "some" of the soldiers in the post were thought to have aided the attackers, though this could not be verified by an independent source and the Taliban did not mention insider help in their statement.
A hunt was underway to release the kidnapped troopers, a defence ministry official in Kabul said.
Casualties among Afghan soldiers and police have increased in recent years as they take more responsibility in the fight against insurgents before their Western allies, the US and NATO troops, leave under a US plan by the end of the year.