WDAM-TV reports 33-year-old Robert Jason Teall is wanted for aggravated assault in the Wednesday night shooting.
Lamar County Sheriff Danny Rigel says the child was dancing in front of the TV when he yelled, and his mother entered the room to find him on the floor. A hospital initially identified his injuries as a laceration and not a gunshot wound.
The mother called authorities after she noticed a bullet hole in the front door and a bullet in the refrigerator.
Authorities believe Teall shot a gun from another house. The bullet then went through the front door, struck the child and lodged into the refrigerator.
It's unclear if Teall has a lawyer.