Columbus police spokesman Sgt. Rich Weiner says the suspect confronted one victim inside the building near Miami-Jacobs Career College.
He said other people inside intervened and took away one knife the suspect was using.
Weiner says those who intervened didn't realize suspect had a second knife.
Three male victims are in critical condition, while a fourth man has minor injuries. The suspect is in critical condition. His name hasn't been released.
Chuck Vella, a spokesman for the college, said it's not known yet whether any of the victims were students or staff members at the privately run college, which has five other locations around Ohio.
Jason Jackson, who works at Gordon's Gourmet in the building lobby, said he heard that someone had been stabbed, so he ran out of the building.
When he came back to see what was happening, he saw the suspect outside.
"He had a knife, and the police had just pulled up, and they're saying, 'Sir, you need to stop. You need to just put the knife down.' He wouldn't. They drew guns. 'Sir, please put the knife down.' And he kind of lunged at them, so they shot him," said Jackson, 31, of Reynoldsburg.
