The mother, Otty Sanchez, 33, of San Antonio, was taken to a local hospital in critical condition with self-inflicted stab wounds to her chest and stomach, said San Antonio police spokesman Joe Rios.
Investigators took a sword, a machete and a kitchen knife from the home.
Officers also found two children unharmed at the home, though it wasn't immediately clear where they were taken.
Sanchez will be charged with capital murder, Rios said.
A spokeswoman at University Hospital in San Antonio said she couldn't release information on Sanchez's condition, but Sergeant Wes McCourt said her wounds didn't appear to be life threatening.
Rios said that when police arrived, Sanchez was sitting on the couch "screaming that she killed her baby". Police said the three-week old baby was Scott Wesley Buchholtz-Sanchez.
"She mentioned that someone or something told her to do it, she was hearing voices. So that leads us to believe that she was experiencing some type of mental crisis," Rios said. "The baby had obviously been decapitated."
McCourt said she told investigators that the devil told her to kill her son.