A soldier was killed in the raid, and a potential suicide bomber was arrested in a car laden with explosives, a military spokesman said.
Security has increased amid fears for the safety of Christians over Easter.
Hundreds of people have been killed since Boko Haram fighters stepped up their campaign in recent years.
The military said the group had been planning an Easter Sunday attack in the city.
"This operation was conducted following a tip-off from our intelligence," military spokesman Iliyasu Abbah said, quoted by Reuters news agency.
Residents reported gunfire and explosions early on Sunday, but there has been no independent confirmation of the casualties.
Kano has seen a series of attacks blamed on Boko Haram, including a suicide bombing on 19 March - apparently aimed at Christians - which left more than 20 people dead.
The group's deadliest attack so far occurred in the city in January 2012, when a series of bombings and shootings killed at least 185 people.
Boko Haram says its members are fighting to create an Islamic state in Nigeria's predominantly Muslim north.
The group has been blamed for the deaths of some 1,400 people in central and northern Nigeria since 2010.
It is believed also to have a presence in Cameroon, Niger and Chad.
Nigeria is Africa's most populous nation and largest oil producer. It is roughly divided between a mainly Muslim north and predominantly Christian south
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