According to court documents, the condition of the home was unlivable, with no water or electricity.
Montgomery County Fire Captain Zachary Adams said the baby boy was healthy and was taken to a local hospital.
It's the 36th baby box in Kentucky.
Because of his age, and the proximity to a busy Versailles Road, police say the child was in danger.
Melissa Kelley, 33, allegedly brought the child in a dirty diaper, with no food, to a stranger's home
The boy was suffering from a broken leg and fractured skull, and tests showed meth was present in his bloodstream.
She traveled to investigate a job opportunity and "because she needed to get away from everything that was happening at home."
Police say they received a report of a 3-year-old girl wandering without shoes, wearing only a t-shirt and a diaper, and crying for "mommy."
When police arrived, they allegedly found the boy at the top of the apartment stairs, crying and asking for his mother.
A Louisville mother was arrested on Friday evening after police say she abandoned her children for three days in a home without electricity.