Nidia Yolibeth Alvarado, 25, has been charged with capital murder, arrest records said.
Alvarado allegedly strangled the 2-day-old child, put his body in a duffel bag and place it in a trash receptacle, a detective said in the affidavit.
"[Alvarado] stated she saw the baby was crying and she then saw it die," the detective's report said in part.
When the boy's discovery Dec. 23 garnered headlines, hospital staff where the baby was born quickly identified the woman they believed was the mother, the San Antonio Express-News said, adding Alvarado gave the hospital a fake name and birthday.
San Antonio police Sgt. Javier Salazar said detective work and statements from Alvarado's family after the baby was discovered on a trash conveyor belt at the recycling center made it possible to identify the mother.