ACCRA, Ghana—Nigeria's Islamist insurgency on Monday kidnapped some 20 girls just miles from a small town where the group abducted several hundred schoolgirls in April, local officials said, in an attack that exposed the military's absence in an area the president pledged to protect.

The village of Garkin Fulani was preparing for its weekly market early Monday when Boko Haram fighters pulled up in a tractor trailer and began pulling young girls into the truck, said Adu Ibrahim, the area's chairman for a vigilante group called...