Officials said the student, who was dressed in black with black-painted finger nails, walked through the school armed with two revolvers as terrified students hid in cupboards and under tables.
One student, 18-year-old Darnell Rodgers, said: "I felt my arm burning ... [and] realised I had got shot."
He was taken to hospital and treated for a wound to his right elbow.
Coon is reported to have made threats in front of students and teachers a week ago.
Parents have been angered by the fact firearms had been brought into the school despite it being equipped with metal detectors, but students said the machines were only used intermittently.
The incident comes just months after a student killed 32 people in Virginia Tech campus in Blacksburg.
The first person to be shot, student Michael Peek, had punched Coon in the face before the shootings began, said student Rasheem Smith.
SuccessTech Academy is a high school in the public school district that stresses technology and entrepreneurship.