The mother, who is at Gwinnett Medical Center, is not expected to survive, WSB-TV reported.
Police responded to the 2700 block of Tybee Drive near Buford about 11 p.m. Sunday after they got a call from the homeowner.
“The caller reported that his son had choked a mother and child that live at the house and walked a short distance up the street to a gas station,” Gwinnett police Cpl. Deon Washington said.
Both victims were taken to the hospital, where the child later died.
The incident happened while the homeowner was outside working on a car in the driveway, Washington said. The woman was renting a room at the home, the homeowner told authorities.
Police confronted the suspect at the gas station and arrested him without incident. Brandon Williams, 32, of Buford, is in the Gwinnett County Detention Center without bond on multiple charges, including one count of felony murder and two counts of aggravated assault.
"Fortunately, this was an isolated incident and police are not searching for any additional suspects,” Washington said.
There are no family ties between Williams and the victims, according to police.
“Detectives are exploring a motive for the homicide,” Washington said.
The names of the mother and her son have not been released.