One of those killed was a girl aged 12, they say.
Witnesses say the explosion was caused by a bomb in a car in the mainly Christian area of Sabon Gari.
The area has previously been targeted by Boko Haram Islamist militants but it is the first attack on Nigeria's second biggest city for several months.
More than 1,000 people have been killed in Boko Haram attacks this year but the government has said it has pushed the militants back into their strongholds in the north-eastern Borno state.
This is where they seized more than 200 girls last month, in a case which shocked the world and prompted foreign powers to send military advisors to assist Nigeria's army tackle the insurgency.
The street in Sabon Gari was full of revellers and street hawkers when a car exploded.
The BBC's Will Ross in Nigeria says that Sunday's blast was so powerful that all that remains of the car is its engine. The blast could be heard from several miles away.
"At about 22:00 [21:00 GMT], we heard an explosion and immediately mobilised to the scene where we discovered a suicide bomber... Five people, including the bomber, were killed," Kano Police Commissioner Adelere Shinaba said.
He said that the victims were "three men and a girl of about 12".
Kano is the largest city in the mainly Muslim north of Nigeria.
The bars and alcohol-sellers in its Sabon Gari area have been targeted on numerous other occasions.
In January 2012, about 150 people died there in a series of co-ordinated attacks by Boko Haram.
The group is fighting to overthrow the Nigeria government and create an Islamic state.
But it has often attacked Muslims, including preachers who disagree with its interpretation of Islam.
The Nigerian authorities are continuing the search for the kidnapped schoolgirls kidnapped.
The abducted schoolgirls, who include Christians and Muslims, were seized on 14 April.
Boko Haram released a video last week showing more than 100 of the girls and offering an exchange for prisoners.
African leaders meeting in Paris at the weekend agreed to wage "war" on Boko Haram, pledging to share intelligence and co-ordinate action against the group.
French President Francois Hollande called Boko Haram a "major threat to West and Central Africa", and said it had links with al-Qaeda's North-African arm and "other terrorist organisations".
The unrest in Nigeria has not just been confined to the north.
Earlier this month a car bomb in the capital Abuja killed at least 19 people and injured 60 more.
The explosion happened close to a bus station where at least 70 people died in a bomb blast on 14 April.
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