The fight happened Saturday morning at Hapeville Elementary School.
The parent said she and her son ran for safety when they saw someone pull out a gun.
"Parents (were) running screaming, crying, trying to get somewhere safe, not knowing if the person that had a weapon, if they were going to shoot or not," she said.
Witnesses said the video shows a coach, wearing red, punch another coach minutes after their teams played each other.
A game for the Georgia Youth Football Alliance had just finished and the 5-year-old players were still on the field.
"The parents and the coaches were angry about the results of the game," the parent said.
Parents shared the video with WSB in hopes of highlighting a lack of security at the games. They said Hapeville police responded but most of the people involved had left.
"There's never any security so you don't know who's bringing weapons into the football games," she said.
Now, the parent said, she doesn't want to see the coaches involved in the fight working with any more children.
"I think you should set a better example if you're a coach," she said.
Right after the fight happened, parents said another group of kids who saw it all were forced to play their scheduled game.
There is no word yet from Hapeville police about whether charges were filed against anyone.