During her confession, Morales-Rodriguez told police said she cut her hands while trying to remove the baby and showed detectives the cuts, then worried that "her children would think their mother was a killer," the charging document states.
The suspect is the mother of three other children, neighbors said.
ABC News affiliate WISN reported Morales-Rodriguez had fooled her boyfriend into believing the child was his.
Last week he wrote on his Facebook page, "My child was born yesterday and he died an hour after birth. He would have been so cute. My woman is shattered, she doesn't stop crying."
Over the weekend, neighbors who lived near Morales-Rodriguez told WISN they were shocked.
Jacqueline Bonilla told WISN, "There's no way, shape or form somebody should hurt somebody else and take somebody's baby just to have one for themselves."
Neighbor Nicole Soto, interviewed while holding her 1-year-old son, had thought Morales-Rodriguez was pregnant.
"She was rubbing her belly all the time. She was telling everyone she was, she was getting bigger," Soto said.
Keila Perez, who shares a backyard with Morales-Rodriguez, told the station, "It's horrible I can't even … I can't think of it I just can't see her doing anything like that."
"She's the godmother of my daughter, she has three beautiful kids that she raised by herself and she's been basically married for four years," said Perez. "To me she's a good woman, she's never been in no problems."
The rare crime generated headlines a few years ago when a pregnant woman -- also 23 years old -- was murdered in Worcester, Mass. Her baby was later found alive in a New Hampshire hospital.
In this case, however, Christian Mercado, the husband of Ramirez-Cruz, must now plan two funerals.
His stepmother, Darla Guiterrez, spoke to NBC affiliate WTMJ on his behalfbecause Mercado does not speak English.
"He wants everybody to remember that she was a good person. She never did anything bad to anybody and she would help anybody out if they needed help," Guiterrez said, adding that the family did not know the suspect.
"We still can't believe it. We know it's true but we can't believe it and the whole family is taking it real hard," Guiterrez said.