Police said the shooting took place on Thursday morning in the bank's lobby and loading dock.
Police said they were "investigating active shooter/officer involved shooting incident at Fifth Third Bank", Presstv Reported.
According to reports, at least four people were shot by the gunman before he was shot by the police.
A city councilman said the suspect was in critical condition.
“What a sick, tragic way for this day to begin. The scourge of gun violence leaves only loss,” council man PG Sittenfeld wrote on Twitter, adding that there were fatalities. The gunman’s motive was not clear, Sittenfeld said. Police said the suspect had been "contained."
WKRC television reported that four victims were admitted to one area hospital.
A large police presence cordoned off a portion of the city's downtown, and several ambulances could be seen at the scene.