Anderson County Sheriff's Office spokesman Chad McBride on Saturday identified the girl as 4-year-old Zoe Brown of Marietta, Ga.
McBride said 31-year-old Alonzo Brown was arrested Saturday, as was the child's mother, 37-year-old Tongela Denise McBride. Both are facing charges of unlawful neglect of a child.
Alonzo Brown was arrested in Anderson County. At a court appearance Saturday, his request for bail was denied.
Tongela McBride was arrested in Georgia and is awaiting extradition to South Carolina;
McBride said the girl is still under foster care. Zoe was left in a stroller Tuesday night on the doorstep of an Anderson home. The homeowner said he didn't recognize the child.