The army said its soldiers were conducting air patrols on Sunday when they spotted a group of people in the northwestern state of Kaduna and confused them with an armed group in the area.
A march mistakenly shelled the village of Todon Beri as residents took part in a festive event.
Official sources said at least 85 people were killed and 66 wounded.
President Paula Ahmed Tinobu has requested an investigation into the incident.
Amnesty International said more than 120 civilians were killed in Sunday's incident.
It stressed in a statement that the Tenobo administration should "immediately" conduct an independent investigation and "where such investigations indicate criminal responsibility, it must ensure that suspects are brought to justice in fair trials."
The chief of the defense staff, Gen. Christopher Guabin Musa, said on national television the same day that "mistakes happen," calling for an increase in the army's budget.
Tinobu has made tackling insecurity a priority since taking office in May, as he seeks to encourage foreign investment in Africa's most populous country.
Nigerian troops often rely on air strikes in their battle against bandit gangs in the northwest and northeast of the country.