The blast happened at the Federal College of Education in the town of Kontagora, Niger state, some 150 kilometres (90 miles) from the state capital, Minna.
There was no immediate claim of responsibility but the explosion happened just two days after nearly 50 students were killed in a suspected Boko Haram suicide bomb attack at a school in the northeastern state of Yobe.
That massacre was one of the worst in the five-year insurgency against a school teaching a secular curriculum, to which the Islamists are opposed.
"We have dispatched our teams from here," he told AFP.
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Student Mary Okafor said the blast happened as they were sitting end of semester exams and saw everyone rush out of class.
"We saw bodies on the ground between the library and the female hostel. Among the bodies were two dismembered women who we believe were the bombers," she added.
"At least 10 students were killed and several others injured," said Okafor.
"They have all been moved to the general hospital. We have all been asked to vacate the school. The authorities in the town have asked all schools to close."
Educational establishments in northern Nigeria have been hit several times by bombings in recent months.
On September 18, at least 13 were killed in Kano during a shoot-out between police and suspected suicide bombers, again at a teacher training college.
A female suicide bomber killed six on July 30 when she detonated her explosives at a noticeboard on the campus of the Kano Polytechnic College while students were crowded around it.
The attack was the fourth by a female bomber in the city in a week and prompted the authorities to cancel public celebrations marking the end of the Muslim holy month of Ramadan.