The first explosion on Wednesday evening took place at a prayer ground in the Muna Gari suburb of the regional capital, Maiduguri.
Other attacks followed in the same neighbourhood.
"At about 6:13pm local time (17:13 GMT), four suicide bombers - two males and two females - infiltrated Muna Gari community and detonated IED strapped to their bodies at different locations," Victor Isuku, Borno State Police Command spokesman, said in a statement.
"A total of eighteen persons including the four suicide bombers, died in the multiple explosions," he confirmed.
Isuku said those injured were rushed to the University of Maiduguri teaching hospital and the State Specialist Hospital for medical attention.
According to the statement, police patrol and bomb disposal teams promptly mobilised to the scene to sanitise and render the area safe.
The statement also said that order had been restored to the community.
No group has yet claimed responsibility for the attacks.