It was the latest in a spate of attacks on churches and on Christian holidays in the north of the country, which Nigerian authorities and diplomats believe are part of an attempt to stoke a religious conflict.
Security sources said there was sporadic gunfire in other parts of the city which they believe was from attackers who were fleeing from the army at the university.
"I counted at least 15 dead bodies. I think they were being taken to the Amino Kano teaching hospital," the witness, who did not wish to be identified, said, adding that he saw many more people being treated for injuries.
A security source said at least 15 people were dead and a source at the hospital told Reuters by phone that he had seen 10-15 dead bodies brought in with gunshot wounds.
There was no immediate claim of responsibility.
Radical Islamist sect Boko Haram, which wants to carve out an Islamic state in northern Nigeria, has killed hundreds in bomb and gun attacks this year. It mainly targets police and authority figures but has also attacked churches.
The army said it had secured the area but could not say how many people had been killed.
"The attack took place in one of the lecture theatres used as a place of worship by Christians. For sure there are casualties but I can't say how many," Ikedichi Iweha, an army spokesman, told Reuters.
"The elements came, used explosives and guns to attack them. We have repelled them and cordoned off the area," Iweha said.
Red Cross officials said they were trying to get access to the area but there were no details on casualties.
BOMB EXPLOSIONS
"For over 30 minutes a series of bomb explosions and gun shots took over the old campus, around the academic blocks," said Mohammed Suleiman, a history lecturer at the Bayero University.
"It started at about 0930 (0830 GMT) this morning ... our school security men had to run for their dear lives. You can see smoke all over," Suleiman said.
Clashes between Boko Haram gunmen and security forces have flared up several times in Kano since the sect killed 186 people in January, its deadliest attack so far.
On Easter Sunday, 36 people were killed when a suspected member of Boko Haram attempted to force a car packed with explosives into a church compound during a service in the northern town of Kaduna.
After being stopped by security he turned back and the bomb exploded by a large group of motorbike taxi riders.
Boko Haram set off a series of bombs across Nigeria on Christmas Day last year, including one at a church outside the capital Abuja that killed at least 37 people.
Africa's most populous nation of more than 160 million is split roughly equally between a largely Christian south and a mostly Muslim north.
Suicide car bombers targeted the offices of Nigerian newspaper This Day in the capital Abuja and in Kaduna last week, killing at least four people in coordinated strikes.
This Day is based in southern Nigeria and is broadly supportive of President Goodluck Jonathan's government - the main target of Boko Haram's insurgency. (Additional reporting by Mike Oboh; Writing by Joe Brock; Editing by Susan Fenton) See Chick's MEN OF PEACE?