Students and staff fled Kano's Federal College of Education as shots rang out and an explosion shook the campus at about 2 p.m. (1300 UTC).
According to the AFP news agency, at least 13 people were killed and 34 injured as police fought a battle with the suspected Boko Haram attackers.
Kano police commissioner Adelere Shinaba described the gunmen as insurgents and said they had run onto the college site after exchanging fire with police outside.
"They were obviously suicide bombers. One of our officers shot at one of the gunmen and the explosives on him went off, killing him on the spot," Shinaba said.
Educational establishments in the city - which is the commercial capital of the north and a center of Islamic scholarship - have been hit several times in recent months.
On July 30, a female suicide bomber killed six people at Kano Polytechnic College. The attack prompted authorities to cancel celebrations to mark the end of the Muslim holy month of Ramadan.
Days earlier, another female bomber blew herself up outside a university in Kano after police stopped her from getting inside the campus. A previous bombing on June 23 killed at least eight people at Kano's city's School of Hygiene.
Change of strategy
When it first launched attacks in 2009, Boko Haram - whose name means "Western education is sinful" - mainly targeted Christians, with the aim of establishing an Islamic state. However, since mid-2013, Boko Haram has focused its attacks on government security agents as well as members of both the Christian and Muslim faiths.
Muhammad Sanusi II, the Emir of Kano, said in an interview broadcast on Tuesday that more investment was needed to prevent radicalization and the rise of Boko Haram.
Sanusi, who was appointed in June, said the government in Abuja - which lies in the center of the country - had to tackle social and economic deprivation in the region, stating that the status quo was "fertile ground for breeding extreme ideologies".
"There are grounds for resentment and then it's very easy for people to come up with all sorts of lunatic ideas and people accept them," said the emir. "As long as people are gainfully employed, they're not likely to jump onto the bandwagon of insurgency."
rc/mkg (AFP, AP, Reuters)