The incident happened over the weekend at Trailblazer Park in Newton County.
The father told WSB-TV that he was at the park with his two children, his mother and his grandmother when the 21-year-old naked man approached them.
The father, Tae Lovelace, said he told the man to leave several times before he grabbed his gun and chased the man. He was able to hold the man while another family member called police.
"Not only did he come back naked he ran directly up to my kids, and the mother of my child and they were frightened," Lovelace said.
He said there were children at the playground while he and his family were at the park to feed the less fortunate through his church.
"I asked him, 'Would you please leave the scene you're causing trouble. You don't even have on any clothes,'" Lovelace said.
Lovelace said the man left the park at around 5:30 p.m. but then he came back.
"It's a family event so everybody out here was pretty much frightened and, at that point and time, I go and get my firearm," Lovelace said.
Lovelace told Covington police that his grandmother called 911 while he chased the man.
That's when he started recording with his phone for officers who arrived within minutes and ordered Lovelace to put down his gun.
"While the cop has his firearm toward me, the guy gets up and runs away again and jumps in the river," Lovelace said.
Other officers then arrested the suspect identified as Josten Meeler.
Police charged Meeler with child molestation, public indecency, and being under the influence of alcohol or drugs.
"Had I not been licensed to carry at that moment who knows what this guy could have done to my family or any of the other families that were here," Lovelace said.