The fighting erupted during the celebrations marking the end of the Muslim holy month of Ramadan.
Criminal gangs, known as yandaba, clashed in seven densely populated neighbourhoods in a district known as Old Kano, on the outskirts of the city, ThisDay newspaper reported.
Soldiers and police were deployed to prevent further violence, residents said.
First outbreak since October
The police would not comment on the reports and there was no immediate confirmation of the nine deaths.
A foreign ministry official confirmed to the French news agency AFP that four people had been killed.
"The fighting lasted more than two hours and four people were killed and many others were injured," the official, Awwalu Mohammed, said.
It was the first outbreak of violence since October, when dozens were killed in clashes between the Muslims and Christians after Muslim fundamentalists protested against the US-led military campaign in Afghanistan.
Interethnic tension
In a separate incident in Kano, ethnic Igbo who live in the north of the city have protested the killing last week of one of their men by angry Muslims.
The Igbo Community Association wrote a letter to President Olusegun Obasanjo saying that the killing of Uche Nwama Ochukpue, a Christian, had been a "symbolic act."
"We are persuaded that this latest murder was a symbolic act, a deliberate message," the letter said.
"The message seems clear enough: the Igboman is not wanted in Kano and can enjoy no protection in the state as he can be killed and dispossessed at will."
Ochukpue, a truck driver, was beaten to death by angry Muslims after driving his truck over a copy of the Koran, the Muslim holy book.
Reports say the incident happened when he was reversing through a market and accidentally ran into a religious study group, one of whose students dropped the book while getting out of the way.