The Nigerian army meanwhile said it had retaken some villages from the Islamist group in the Lake Chad region in operations on Friday and Saturday and “rescued” 85 people, including women and children. It also claimed nearly 40 Islamists were killed in other operations.
A group of Boko Haram gunmen arrived in Akwada, 10km from Chibok, late Saturday and torched homes after looting food supplies.
The attack came just hours after the army said it had rescued one of the missing Chibok schoolgirls with her 10-month-old baby near the Cameroon border.
“Boko Haram gunmen attacked the village around 19:30. They fired indiscriminately and hurled explosives,” resident Bitrus John told AFP.
“They killed two soldiers and injured another one in gunfight,” he said.
Troops patrolling the area engaged the Islamists in a shootout, allowing residents to flee the village unhurt, said John.
Soldiers had deployed in the village following incessant attacks in the area in recent months.
“The village has been entirely burnt, there is nothing left apart from burnt rubble of our mud houses,” said Bulus Samson.
The attack underscores the continued threat of Boko Haram in Nigeria’s volatile northeast, where the military is battling for control despite making gains against the insurgents over the past year.
It came two weeks after similar raids on two nearby villages where the Islamists looted and burnt homes.
The Nigerian army said on Sunday it had rescued 85 people held by Boko Haram in villages around Lake Chad.
Army spokesman Sani Usman said in a statement that five insurgents and a soldier were killed and that weapons had also been recovered.
Usman said 37 Boko Haram fighters were killed in another operation in four villages in the south of Borno state, the epicentre of the Islamist uprising.
He said a local vigilante died and five soldiers were wounded during the operation.
Boko Haram’s seven-year insurgency in Nigeria’s predominantly-Muslim north has claimed at least 20 000 lives and made more than 2.6 million homeless.
Nigerian troops with the help of neighbouring countries have recaptured swathes of territory from Boko Haram since early 2015, but the extremists have carried out sporadic attacks on remote villages in the restive region.