The latest violence came as the government announced the arrest of a 10-year-old girl with explosives strapped to her chest in a neighbouring area.
Boko Haram is blamed for killing more than 10,000 people since 2009 and their extreme tactics have been denounced worldwide, including on some jihadi websites.
But what appears to be a new tactic of deploying young women and girls as bombers will spur further outrage, as Nigeria seems unable to contain the violence.
Witness Isyaku Adamu said the explosion came from within the crush of students and left blood splattered on the ground, as soldiers and police scrambled to secure the area.
Government spokesman Mike Omeri put the casualties at six dead and six wounded and confirmed that a female, whose age was not immediately known, was responsible for the bloodshed.
It was the fourth attack by a female bomber in Nigeria's second city since the weekend.
The next day, two young women believed to be in their late teens or early 20s separately attacked a petrol station and a shopping centre, suicide blasts that killed at least three people and injured 13 others.
Omeri said security forces yesterday stopped a car in Kano's neighbouring state of Katsina and arrested three suspected Boko Haram members.
The group included one male and two girls, aged 18 and 10.
The older two tried to flee, according to Omeri's statement.
The chilling trend of deploying young women and girls as bombers comes three-and-half months after Boko Haram kidnapped more than 200 schoolgirls from the remote town of Chibok in the northeast.
Boko Haram leader Abubakar Shekau boasted about the mass abductions in a video during which he threatened to sell the girls as slaves.
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