The attack took place in an "isolated area" of Lokoja, capital of Kogi State, according to a statement by the state's commissioner, Kingsley Femi Fanwo.
He said 15 children were later rescued.
The facility, Dahallukitab Group of Schools, was operating illegally, Fanwo said.
No group immediately claimed responsibility for the attack. The region has seen an increase in kidnappings for ransom.
The statement did not say how old the abducted children are, but the term "pupil" in Nigeria usually refers to someone in kindergarten or primary school, covering ages up to 12.
"Intensive operations are ongoing to secure the safe return of the remaining eight victims and apprehend the perpetrators," Fanwo said.
Students' kidnappings have come to define the insecurity in Africa's most populous nation.
In November, more than 300 students and their teachers were abducted from one Catholic Secondary School in Niger State, also in the north central region of Nigeria.
They were released in two batches with the last group regaining freedom more than one month after.Â
Analysts say armed gangs see schools and students as "strategic" targets to draw attention.
with EFE
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