According to Agence France Presse, gunmen carried out the attack on Monday after blowing up part of a primary school in the town of Damagun, Yobe State, the day before.
Police officers were able to fight the gunmen as they attacked the school and the Damagun police station.
According to police, there were no casualties in the attacks.
It is not clear who is behind them, but suspicion has fallen on Boko Haram, the militant Islamist group that has claimed responsibility for previous attacks on church and civic buildings across northern and central Nigeria.
The group has stated that it wants to impose sharia law and eradicate Christians from the region.
Nigeria is divided roughly between a largely Muslim north and predominantly Christian south.