Three of the injured remained hospitalized in critical condition Wednesday night, authorities said at a news conference.
"The fair is about the best things in life, and tonight with this accident it becomes a terrible, terrible tragedy," said Republican Gov. John Kasich.
The man who was killed was one of several people who were thrown when the ride malfunctioned, Columbus Fire Battalion Chief Steve Martin said earlier.
Dramatic video captured by a bystander shows the ride swinging back and forth like a pendulum and spinning in the air when it crashes into something and part of the ride flies off, throwing riders to the ground.
A company providing rides at the fair this year describes the Fire Ball as an "aggressive thrill" ride.
On its website, Amusements of America says that since its debut in 2002, the Fire Ball has become "one of the most popular thrill rides on the AOA Midway." The company description of the ride says it swings riders 40 feet (12 meters) above the midway while spinning them at 13 revolutions per minute.
The company did not immediately return a phone message seeking comment.
Kasich said he has ordered a full investigation and also ordered that all fair rides be shut down until additional safety inspections can be completed.
The fair did not immediately respond to an email seeking comment. In a post on its Twitter page it said: "There has been a report of a ride incident. We are investigating and will report information as available."
The Ohio State Fair runs through Aug. 6.