Security sources said gunmen arrived on motorbikes and threw small homemade bombs into the theatre before shooting fleeing worshippers. There was sporadic gunfire in other parts of the city later on from attackers driven from the university by the army, the sources said.
"I counted at least 20 dead bodies. I think they were being taken to the Amino Kano teaching hospital," said a witness who did not wish to be identified. He said he saw many more people being treated for injuries.
A security source said at least 20 people were dead and a source at the hospital said by telephone he had seen 15-20 dead bodies brought in with gunshot wounds and dozens more wounded were being treated.
Bayero University spokesman, Mustapha Zahradeen, said two university professors had been killed in the attacks.
There was no immediate claim of responsibility.
Radical 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.
"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," said Ikedichi Iweha, an army spokesman.
"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 and had no details on casualties.
"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 near 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.
Jonathan has been criticized for failing to get a grip on the sect's wave of violence, which has gained momentum since his presidential election victory a year ago.
The president has relied mostly on a heavy-handed military approach to dealing with the violence and an attempt at mediated dialogue with the sect broke off last month after details of negotiations were leaked to the media.
On a visit to the This Day bomb site in Abuja on Saturday Jonathan refused to be drawn on whether talks with Boko Haram were ongoing but he did not count them out.
"Just like a war situation, you may dialogue, you may not dialogue, depending on the circumstances. But we will exploit every means possible to bring this to an end," Jonathan told reporters.
