The attacker was disguised as a student when he set off the explosion in a government boarding school in the town of Potiskum, police spokesman Emmanuel Ojukwu said.
"We suspect Boko Haram is behind the attack," Ojukwu said.
The explosion took place at 7:50 a.m. local time outside the principal's office, where students had gathered for a daily speech.
"We were waiting for our teachers to come and address us at the assembly ground when we heard a huge explosion," student Adamu Ibrahim said.
It was not immediately clear how many of the casualties were students.
Although no one has claimed responsibility for the attack, Boko Haram
is the prime suspect.
The radical Islamic militant group has carried out deadly attacks on schools teaching Western curriculum.
In February, Boko Haram gunmen killed at least 40 students when they opened fire and threw explosives in student hostels in a government boarding school in the town of Buni Yadi, in Yobe state.
And last year, 42 students were killed when Boko Haram gunmen attacked dormitories with guns and explosives in a government boarding school near Potiskum.
Potiskum, the commercial hub of Yobe state, has been repeatedly targeted by deadly attacks blamed on Boko Haram.
Just last week, a suicide bomber blew himself up in Potiskum amid a large crowd of Shiite Muslims
holding the annual Ashura ceremony to commemorate the murder of Imam Husseyn, the grandson of the Prophet Mohammed.
That blast killed 15 people. No one claimed responsibility for the attack, but Boko Haram was suspected.
The group's five-year insurgency is aimed at establishing an Islamic state.