The 37-year-old was arrested on Friday after a lengthy investigation which started in November.
The baby, Alexis, was found dead after a 911 call brought paramedics to her Campobello home, WYFF 4 News reported.
The medical examiner later found the baby girl died from a lethal dose of morphine, which she ingested through her mother's breast milk.
"Doing toxicology tests and things like that, we wanted to make sure, and the coroner's office wanted to make sure that we had done everything correctly and possible to make sure we understood fully what had happened to this child, how this child died and who was responsible for it," Tony Ivey of the Spartanburg County Sheriff's Office told WYFF 4 News.
Police later found that Greene used fake prescriptions to obtain the drugs, including Fentanyl and Hydrocodon, starting in 2009. She began taking pills and used patches containing morphine around the time baby Alexis was born, according to WFMY 2 News.