Gunmen opened fire on a checkpoint in the southern state, then drove to two police stations, killing officers and burning patrol cars, police say.
Police killed two of the attackers but are searching for those who escaped.
It is not clear who was behind the killings, but the region has seen a surge in separatist attacks on police.
The unidentified armed men, driving a Toyota Hilux van, launched their “surprise assault” on the checkpoint at Choba Bridge at around 20:30 local time (19:30 BST) on Friday, police spokesperson Nnamdi Omoni said.
After shooting dead two police officers at the checkpoint, they killed two more officers and set fire to a patrol car at Rumuji police station, Mr Omoni said. Police fired back there and killed two of the attackers, he said.
The remaining gunmen then killed three more officers at the Elimgbu police station, he added.
A number of police officers and soldiers have been killed in the region in recent weeks, prompting a night-time curfew.
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