The attack is the fourth mass kidnapping of schoolchildren since December.
Criminal gangs, which had previously focused on cattle rustling, have switched to targeting educational facilities since the start of the school year.
An investigation by local media found that 1065 students have been kidnapped by bandits in Nigeria over the past seven months.
Six of the children have been killed by their abductors, while more than 250 are still held captive.
Most are eventually returned home after ransom is paid following negotiations with local officials.
Emmanuel Paul, a teacher at the Bethel Baptist High School, said that 25 students had managed to escape after being taken from the boarding school.
Mohammed Jalige, a local police spokesman, said that "tactical police teams" were pursuing the kidnappers.
Gunmen also frequently target hospitals in the region. In April, two nurses were snatched from a hospital in the Kajuru area of Kaduna State.
The state governor, Nasir El Rufai, has said he will not negotiate with kidnappers and blames the increase of incidents on criminals from other regions.
However, his recent move to withdraw his son from a local school after he was put there to inspire confidence has emboldened critics who believe the situation is getting out of hand.