Humberside Police were called to reports of a man in Hessle Road in possession of a firearm in the early hours of Sunday morning.
The force confirmed he had been shot by an officer.
No one else was injured.
Police confirmed the incident was not terror related and transferred the case to the Independent Office of Police Conduct (IOPC).
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.
"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."