Colonel Sakhidad Haidari, Head of Badakhshan police said the incident took place Saturday when the vehicles were delivering foods to Yawan district when the militants stopped them on the way back.
Haidari added, the drivers of the vehicles were detained by militants but later they were released.
According to reports, the militants belonging to Mawlavi Safiullah, one of the commanders of Taliban group.
However, WFP has not released details regarding the incident so far.
This attack comes only two days after the convoy of another UN agency was attacked in eastern Nangarhar province.