The attacks happened on Sunday night, and one of the suicide bombers targeted the University of Maiduguri, the Xinhua agency said.
Borno Police Commissioner Damian Chukwu said that police had arrived at the scene, and those injured were taken to the hospital.
Nigeria is the heartland for Islamic extremist Boko Haram group that rejects the Western model of education and presses for Nigeria to switch to Sharia laws. The group is behind most of the acts of terror committed in the country. Niger, Cameroon and Chad are carrying out a military campaign against Boko Haram, and they also host about 250,000 refugees from Nigeria displaced by the conflict.