Suspected gunman Omar Enrique Santa Perez, 29, is seen in bank video footage walking through the lobby of the Fifth Third Bank building in Fountain Square Thursday morning "firing shots at anyone he sees", Isaac said.
The suspect was shot multiple times as four police officers approached.
The motive of the shooter, whose identity has not been released, was not known.
Cincinnati Mayor John Cranley said the gunman was "actively shooting innocent victims" and that it was a "horrific" scene.
Police have not yet determined whether he was killed by officers or by a self-inflicted gunshot. Each had gunshot wounds, officials said.
The building is home to Fifth Third Bancorp's headquarters along with a number of other businesses, including ice cream, pastry and sandwich shops.
One of the people wounded was in fair condition Friday and another patient was in serious condition at University of Cincinnati Medical Center.
Police said the gunman, a Cincinnati-area resident since 2015, wasn't a current or past Fifth Third employee.
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A witness said a woman walked into the bank wearing headphones, and she did not hear warnings not to enter.
Bank manager Greg Harshfield, who on the 29th floor of the building when the shooting began, said that he heard multiple shots and saw police arrive nearly immediately.
"There was definitely a lot of blood involved", he said. "After that, I started running", Richardson told the paper. Isaac said the shooting took place in the building's loading dock and then the lobby.
The chaos unfolded alongside Fountain Square, the heavily trafficked park at the city's center.
'Our family has been overwhelmed by the support we have received from co-workers, family, friends and total strangers, ' she said.
People were also asked to avoid the area around Fountain Square.
"Oh, no, no, no, no", the woman said as she slumped against the wall and spoke to Perez's sister.
"All he had to is look over the counter at us and we would have been shot", Ginyard told reporters.
"Terrible shooting incident in the heart of our city this morning", City Councilman P.G. Sittenfeld tweeted.
Manager Duhaney gives credit to police for "swift and decisive actions" that played a role in keeping this incident from being "much worse".