Police found the body of Frank Q. Jackson, 24, near a public-housing project in the city on Sunday night. According to news reports, the mayor visited the shooting scene before leaving.
The Cleveland Division of Police Homicide Unit is investigating, though police released little information about what happened.
Authorities were seeking a suspect in the shooting.
Frank Q. Jackson faced several charges over the years. In July, he pleaded not guilty to an indictment for felony assault and failure to comply with police.
He was free on $10,000 bond while he awaited a court appearance for a felonious assault charge in which he was accused of dragging a police officer while trying to flee his car in January.
In 2019, he pleaded guilty to misdemeanor assault stemming from a fight with his then-girlfriend. He was sentenced to 18 months probation.
Anyone with information is asked to call investigators at 216-623-5464. Anonymous information can be provided by calling Crime Stoppers at 216-25-CRIME. Police said a cash reward of up to $5,000 may be available.
The Associated Press contributed to this report.