The group includes 27 students, three teachers and nine family members, the state government said in a statement naming them all.
One student who died during the attack was named Benjamin Habila.
Niger Governor Abubakar Sani Bello he closed all boarding schools in the area and sent the army to rescue those abducted from school, according to its chief press secretary, Mary Noel Barje.
President Buhari has condemned the abduction of school children.
“The president has instructed the Armed Forces and the police to ensure the immediate and safe return of all captives,” Buhari spokesman Garba Shehu said in a statement on Wednesday.
“The president also sent a team of security chiefs to Minna, Niger State, to coordinate the rescue operation and meet with state officials, community leaders, as well as parents and college staff.”
A former Nigerian senator, Shehu Sani, told CNN that the school does not have a perimeter fence and would have allowed easy access to militants.
Sani, who was also a student at the school, told CNN: “The city is at the epicenter of the Niger insurgency. Fulani bandits operate within the axis and there are thousands of people displaced in this area. Bandits in northwestern Nigeria are becoming more lethal and more destructive than Boko Haram. ”
Buhari recently withdrew all heads of security forces in Nigeria and named new ones amid growing insecurity and kidnappings in the country.
“Nigeria’s security situation is” overwhelming and threatens the country’s peace, “Sani told CNN.
“It is unfortunate that the heads of services have been allowed to stay so long,” he added.