Rahmatullah Khan Faqirzada, governor of Kalakan District said the bomb had been placed on a roadside in Babush area, adding that it exploded as the ANA vehicle reached there.
No one has been arrested in connection to the blast but Faqiradad said that an investigation was initiated.
Earlier, a bomb blast injured three soldiers in eastern Nangarhar province.
The explosion took place in Naranj Bagh area of Jalalabad city, the provincial capital of Nangarhar, and those wounded belonged to Afghan National Civil Order Police (ANCOP).
There is no word of responsibility for both attacks.