The attack, which happened on Monday at the Lassa Day Secondary School in the Askira-Uba area of Borno state, left at least one teacher dead.
Twenty-five girls and 11 boys, as well as three teachers were abducted during the attack, Dauda Iliya, spokesman of the governor of Borno, said in a statement.
The governor, Babagana Zulum sent a delegation of high-level officials to the community. It was not immediately clear if the teachers were rescued.
Borno education commissioner Lawan Abba Wakilbe described the incident as "unfortunate" and said the authorities were working with security agencies and community leaders to ensure the safe return of the missing students and staff.
The students, who were taking their secondary school leaving examinations when they were attacked and abducted, are between 15 and 18 years old.
No group immediately claimed responsibility for the attack but an insurgency from armed groups in the region has killed thousands and displaced millions.
Boko Haram and its splinter faction, which is affiliated with the Islamic State group and known as Islamic State West Africa Province, or ISWAP, are prominent militant groups in northeast Nigeria and the greater Lake Chad area, which is bordered by Chad, Niger Republic and Cameroon.
Earlier this month, the Nigerian army rescued more than 300 people abducted by Boko Haram from Ngoshe, a town about 114km from Lassa, where the abduction happened.
In May, the West African country said its joint operation with the United States had killed 175 ISWAP fighters.
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