According to a police statement, the shooting began at 1.00 am local time in the city's Oregon District, which is home to a number of bars and restaurants.
At least 16 others have been brought to hospital with injuries.
Dayton Police have now confirmed that the shooter is dead, and the FBI are at the scene assisting in the investigation.
"We had officers in the immediate vicinity when this shooting began and were able to respond and put an end to it quickly."
One witness, James Williams, who said he was sitting outside the bar at the time of the incident, recalled a man carrying a rifle approaching the area before opening fire.
He said on Facebook: "The active shooter he tried to go into the bar but did not make it through the door someone took the gun from him and he got shot and is dead.
"A bunch of people was taken to hospital I don't know how many this place is a disaster."
In a further video to Facebook, Mr Williams added: "It's awful. I've never seen anything like this."
In a tweet, Dayton Police Department advised people to avoid the Oregon District area of the city as an investigation continued.
It added: "This is a large scene and investigation."
We will provide information and facts regarding the #OregonDistrict shooting through this account as they become available. This is a large scene and investigation. Thank you for your patience.
— Dayton Police Dept. (@DaytonPolice) August 4, 2019
