The man shot by police Hessle Road remains in a "critical but stable" condition as officers confirm an arrest has now been made.
The busy street was closed just after 1am on Sunday after reports of gunshots ringing out through the residential street.
A large police cordon was put up by officers who rushed to the scene, before blocking off the part of the road.
During the incident, a 35-year-old man was shot by police and remains in hospital being treated for serious injuries. The shooting has prompted two separate investigations to be launched - the police's criminal inquiries and the Independent Office for Police Conduct's (IOPC).
While the man continues to fight for his life, the IOPC is undertaking an independent investigation into the actions of Humberisde Police officers - something the force say they are fully cooperating with.
Providing an update on Tuesday, the force have confirmed a man has been arrested "on suspicion of firearms offences" and will be interviewed "in due course".
In a statement, assistant Chief Constable Chris Noble said: “Officers were deployed to the Hessle Road area of Hull just after 1am on Sunday, December 15, following a report a man was in the street and believed to be in possession of a firearm.
“During the incident, a man was shot by police. He remains in hospital today in a critical but stable condition.
“There are two investigations that are currently running parallel in connection to the incident.
“We are carrying out a criminal investigation in which a man has been arrested on suspicion of firearms offences and will be interviewed by officers in due course.
“The Independent Office for Police Conduct (IOPC) is carrying out a separate, independent investigation that will look into our actions as part of the incident.
“We will fully cooperate with the IOPC’s investigation and evidence gathering and provide assistance in any way we can."
Anyone with information on the incident, who has yet to speak to the police, is asked to call them on 101, quoting log number 178 of December 15.
Speaking on Monday, IOPC interim regional director Dave Ford said: "We have begun an independent investigation following a police shooting in Hull in the early hours of Sunday December 15.
"A 35-year-old man was shot by a Humberside Police officer on Hessle Road after they received reports of a man being in possession of a firearm at approximately 1am. The man remains in hospital where he is being treated for serious injuries.
"We attended the scene and the police post-incident procedures on Sunday and have today confirmed that this will be independently investigated.
"This investigation is at an early stage but we can confirm that we are securing footage of the incident and we will be independently reviewing this over the coming days.
"We will also gather accounts from all police officers and staff directly involved as part of our evidence gathering.
"Our thoughts remain with everyone affected by this incident."
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