The victims have been taken to a hospital. According to BBC, the shooter was also killed.
According to Dayton Daily News, the gunman opened fire using a semi-automatic weapon when he was refused entry to Ned Peppers Bar.
"We had officers in the immediate vicinity when this shooting began and were able to respond and put an end to it quickly," the Dayton Police Department tweeted. "The FBI is on scene to assist in this investigation," they added.
The incident comes hours after a man opened fire at a Walmart store in El Paso, Texas, leaving 20 dead and 26 injured. The incident took place a few miles away from the US-Mexican border and is being investigated as a possible hate crime.