The attack in the troubled state of Katsina occurred according to police late on Friday.
Armed men attacked the school in the Kankara district, at 9.40pm local time, in what is believed to be a kidnapping attempt.
In a statement, Gambo Isah, a local police spokesman, said police opened fire on the attackers, prompting students to flee.
Data on 400 abducted
According to AFP's local sources, several students have been abducted, while two sources told Reuters that about half of the school's approximately 800 students are missing.
Now the police are working with the military to find out if the attackers managed to kidnap some children.
According to the police, it has not been established that students are missing.
They have not yet been counted.
And students are said to have gone to their homes after the attack.
Firefighting has broken out
President Muhammadu Buhari writes in a statement that the military has located the suspected kidnappers and that a firefight has broken out, in which the military has received air support.
The state of Katsina has major problems with criminal gangs that, among other things, feed on thefts and kidnappings in the hope of getting ransoms.