Verna Deann McClain, 30, was charged with capital murder after she confessed to the incident, the Montgomery County Police Reporter stated.
McClain told police she shot and killed the mother, Karla Golden, 28, then kidnapped the her newborn son Tuesday afternoon, police said.
Golden was taking her son to a pediatrician's office near Houston for a routine checkup when the incident occurred, the Houston Chronicle reported.
McClain apparently approached Golden as she was leaving the doctor's office, authorities said. The two began arguing before the suspect allegedly pulled out a pistol and fired at the victim and fled with the child.
The baby was later found alive in the suspect's home.
The Montgomery County Sheriff's Office said Golden died at the hospital, CNN reported
District Attorney Brett Ligon said the baby, named Keegan, was located six hours after the shooting in "safe condition."
Ligon said the infant would be reunited with his father.
Police detained several people for questioning but no charges were immediately filed.