Roger Stephens of Stone Mountain is charged with felony cruelty to children. It was unclear if he had an attorney and a telephone call to his home Wednesday was unanswered.
Authorities say the girl and her mother were shopping Monday when the toddler began crying. The police report says Stephens approached the mother and said, "If you don't shut that baby up, I will shut her up for you."
Authorities say Stephens then grabbed the 2-year-old and slapped her. The child began screaming and Stephens was arrested. Police say an examination showed the girl's face was slightly red.
A call to the girl's mother, identified in the police report as Sonya Mathews of Grayson, was answered by a woman who identified herself as Sabrina Mathis, the victim's aunt.
Mathis said Wednesday that the girl is doing fine.
"As of today, she has really forgotten about it," Mathis said. "She's been playing."
Mathis said the girl's mother was shaken up over the incident.
"She's as well as to be expected," Mathis said. "Right now she's just trying to calm down."