At least 20 others were wounded in the blast at the Kano School of Hygiene.
The city has been targeted in the past by the radical Islamist group Boko Haram, which aims to create an Islamic state in northern Nigeria.
Three states to the east of Kano are under a government-imposed emergency after years of militant attacks.
Kano State police spokesman Magaji Majiya, who confirmed the attack, said eight people had been killed and many others with horrific injuries had been taken to hospital for treatment.
The BBC's Mansur Liman, in the capital Abuja, says the blast occurred as students were struggling to meet a deadline to register for the new academic session.
He says the area has been cordoned off and emergency services are continuing to take the injured to hospital.
One person has been arrested, according to the police.
A teacher at the college told the AFP news agency that the blast seemed to originate from a car park next to the post-secondary training school.
The latest incident comes less than a week after some 21 people were killed in a bomb blast outside a shop in Yobe state where people had gathered to watch a World Cup match.
Public screenings of the World Cup in some parts of Nigeria have been banned because of threats by Boko Haram, who want to overthrow the government.
Boko Haram - which means "Western education is forbidden" in the Hausa language - captured international attention in April after it abducted more than 200 girls in Chibok in Borno state.
The states of Borno, Yobe and Adamawa have been under a state of emergency since May 2013. Thousands have died in the north-east since Boko Haram launched an insurgency in 2009.
Nigeria's military has promised increased security but there are still daily reports of attacks on villages in parts of the north-east.
Kano is the largest city in the mainly Muslim north of Nigeria.
In January 2012, about 150 people died in a series of co-ordinated attacks in the city by Boko Haram.
An explosion has struck a public health college in Nigeria's second city of Kano, in the north, killing at least eight people, police say.