All the victims are members of the same family, police said.
CNN affiliate WSFA said its crew was on the scene when a man approached reporter Cody Holyoke and said, "I'm the guy you're looking for."
The crew immediately left the area, drove to a nearby parking lot and called 911, WSFA said. Police arrived, took the man into custody and searched his white Jeep, according to the station.
Elkins said earlier the shooting was believed to be domestic violence-related and the public was not in danger.
Police didn't provide the relationship between victims and suspect.
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Shortly before 4 p.m. CT, police responded to a report of a shooting on the campus, which is about 60 miles east of Montgomery, Alabama, Elkins said.
Officers found a 36-year-old woman shot in the right arm; a 63-year-old woman who had been shot in the upper torso and was later pronounced dead; and a woman in her 90s who was shot once in the back and once in the neck and was flown by helicopter to Columbus Regional Medical Center in Columbus, Georgia, Elkins said.
In addition to the three adults, a 4-year-old child was cut by flying glass. She was transported to East Alabama Medical Center in Opelika for treatment, police said.
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Officers believe the 36-year-old woman is a student who was being dropped off or picked up, but authorities were still trying to confirm that, Elkins said.
All the victims were from Lee County, where Opelika is located, Elkins said.