Witnesses said the attack hit an old section of the campus of Bayero University in Kano. Abubakar Jibril, a spokesman for Nigeria's national emergency management agency, said at least three explosions had struck on and around the campus, and that sporadic gunfire was continuing on Sunday morning.
Jibril said rescue officials could not reach the site as an attack appeared to be still under way.
A police spokesman referred calls for comment to Nigeria's military. Military spokesman Lieutenant Iweha Ikedichi said soldiers and police had surrounded the university and were searching for the gunmen.
"There were casualties, but I don't have exact figures," Ikedichi said. "Some are injured and have been rushed to local hospitals."
No group immediately claimed responsibility. The attack comes as Nigeria faces a growing sectarian battle between its weak central government and radical Islamist sect Boko Haram.
Diplomats and military officials say Boko Haram has links with two other al-Qaida-aligned terrorist groups in Africa. Members of the sect have also reportedly been spotted in northern Mali, where Tuareg rebels and hardline Islamists have seized control.
The sect has been blamed for killing more than 450 people this year alone, according to an Associated Press count.
In January, a co-ordinated Boko Haram assault on government buildings and other sites in Kano killed at least 185 people. In the time since, the sect has been blamed for attacking police stations and other smaller targets in the city.
On Thursday, it carried out a suicide car bombing at the Abuja offices of influential newspaper ThisDay and a bombing at an office building the paper shared with other publications in the city of Kaduna. At least seven people were killed in those attacks.