Gunmen reportedly arrived at the school in Chibok, Borno state, late last night, and ordered the hostel’s teenage residents on to lorries.
The attackers are believed to be from the Islamist group, Boko Haram, whose militants frequently target schools.
On Monday, bombings blamed on the group killed more than 70 people in the capital, Abuja.
Boko Haram, whose name means “Western education is forbidden” in the local Hausa language, has been waging an armed campaign for an Islamic state in northern Nigeria.
A map showing Borno state and the town of Chibok in Nigeria
A government official in Borno state told the BBC around 100 girls were thought to have been abducted from the school.
The exact number of missing students had yet to be established, as some of the girls had managed to return to their homes.
Parents had earlier told the BBC that more than 200 students had been taken from the school.
Residents in the area reported hearing explosions followed by gunfire last night, said BBC reporter Mohammed Kabir Mohammed in the capital, Abuja.
“Many girls were abducted by the rampaging gunmen who stormed the school in a convoy of vehicles,” AFP news agency quotes Emmanuel Sam, an education official in Chibok, as saying.
Another witness, who requested anonymity, told AFP that gunmen overpowered soldiers who had been deployed to provide extra security ahead of annual exams.
A girl, who managed to escape and wished not to be named, told the BBC she and fellow students were sleeping when armed men burst into their hostel.
“Three men came into our room and told us not to panic. We later found out later that they were among the attackers,” she said.
The girls said she and her schoolmates were taken away in a convoy, which had to slow down after some of the vehicles developed a fault.
Around 10 to 15 girls seized the opportunity to escape.
“We ran into the bush and waited until daybreak before we went back home,” she said.
Nigerian media reported that two members of the security forces had been killed, and residents said 170 houses were burnt down during the attack.
Boko Haram emerged as a critic of Western-style education, and its militants frequently target schools and educational institutions.
This year, the group’s fighters have killed more than 1,500 civilians in three states in north-east Nigeria, which are currently under emergency rule.
The government recently said that Boko Haram’s activities were confined to that part of the country.
However, Monday’s bombings in Abuja prompted renewed fears that the militants were extending their campaign to the capital.
Boko Haram at a glance
• Founded in 2002
• Official Arabic name, Jama’atu Ahlis Sunna Lidda’awati wal-Jihad, means “People Committed to the Propagation of the Prophet’s Teachings and Jihad”
• Initially focused on opposing Western education
• Nicknamed Boko Haram, a phrase in the local Hausa language meaning, “Western education is forbidden”
• Launched military operations in 2009 to create an Islamic state across Nigeria
• Founding leader Mohammed Yusuf killed in same year in police custody
• Succeeded by Abubakar Shekau, who the military wrongly claimed in 2013 had been killed