The shooting happened on the 3400 block of East 140th Street.
Cleveland Police Chief Calvin Williams says officers were called to the area around 9:30 a.m. for a report of one man firing at another man.
A person matching the description of the suspect approached a police officer in a cruiser and pointed a handgun at the officer.
The sergeant, still in his cruiser, ordered the suspect to drop the weapon, which he did not.
At that time, Sgt. Miller fired three times, hitting Kendrick Brown. The 35-year-old man was taken to MetroHealth Medical Center where he died.
It is still not clear if the suspect fired at the police officer. Chief Williams says there were spent casings in the weapon, but it could have been from the earlier shooting.
As in every case involving a police officer involved shooting, the Sergeant Miller has been placed on administrative leave and the prosecutor's office will review all facts.
Like 19 Action News on Facebook for the latest news, weather, sports and giveaways.