One person was killed in the entourage of Mr Sanusi as he returned from Eid prayers on 30 March.
The police say they are probe the killing of a man during Kano Emir Lamido Sanusi's Sallah day procession on Sunday.
The disturbance occurred when Mr Sanusi returned home from Eid prayers on Sunday.
The police and other security agencies in the state had banned the traditional Sallah Durbar procession, "in pursuit of safe and secure celebration and to sustain the relative peace and public order in the state."
The police spokesperson in the state, Abdullahi Kiyawa, announced in a statement on Thursday that the agency had set up a Special Investigation Panel for the probe.
"The panel will examine the causes of the incident and any violations of the police ban on Durbar and horse-riding during the Sallah celebrations.
"The Command had earlier banned all forms of Durbar and horse-riding during Sallah due to security concerns in the state," the statement read.
"The violence led to the death of Surajo Rabiu, a vigilante member from Sabon Titi Jaba Quarters, while another person, Aminu Suleman of Kofar Mata Quarters, was injured and is receiving treatment at Murtala Mohammed Specialists Hospital," the police said.
Mr Kiyawa said the police had arrested two suspects: Usman Sagiru, 20, of Sharifai Quarters, and Nasir Idris, 35, of Kofar Mazugal Quarters in connection to the killing.
Also, Mr Kiyawa said an aide of Mr Sanusi, Wada Isyaku, who holds the title of 'Shamakin Kano', was invited for questioning over alleged defiance of the Durbar ban.
"The panel is charged with expediting action to ensure justice is served, and anyone found culpable will face the full wrath of the law," the statement added.
PREMIUM TIMES observed that the two emirs observed Eid prayer in the city from different locations.
Mr Ado-Bayero performed the Eid prayer at the mini palace with residents and supporters. Mr Sanusi, on his part, presided over the prayer at the Eid prayer ground, Kofar-Mata, with Governor Yusuf and other top government officials in attendance.
Violence erupted in Mr Sanusi's encourage on his way back to the palace when some hoodlums threw sachets of water on the emir, prompting violence quelled by the police firing teargas.
Also, on Tuesday, Mr Sanusi visted Governor Yusuf for the Sallah homage. The visit was delayed due to obstruction caused by the presence of the rival emir on the state road.
Mr Sanusi took a longer route to the Kano State Government House in a convoy of cars to pay Sallah homage to the governor.
The mini palace occupied by the embattled 15 Emir of Kano, Mr Ado-Bayero, is situated on the state road about 300 metres from the Government House. It was also buzzing with Sallah activities as supporters paid homage to the palace.
Security agents barricaded the state road from the main emir's palace (Gidan Rumfa), which is the traditional route Mr Sanusi is expected to follow to the Government House. However, he diverted to another route as Mr Ado Bayero's Sallah event at the mini palace was taking place.
Mr Sanusi took a longer route from the main palace moving through Sabuwar Kofa, BUK Road, Zaria Road, Gadar Lado, and Tarauni Junction.
When returning to the palace, Mr Sanusi rode through Lodge Road, Nasarawa Hospital, Bank Road, Ibrahim Taiwo Road, Kofar Mata and Shahuci.
His supporters were seen in a viral video singing to mock the police's ban on the durbar procession.
"If we can use horses for the Sallah durbar we can use cars," they sang at the Government House.