The incident took place La Villa de Don Fadrique, a village of around 4,000 people near the city of Toledo.
“She killed her baby in the cemetery chapel,” a police source said, adding that the woman had apparently slit the child's throat.
A knife was found at the scene.
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The woman, who also has another child, was arrested at the village church, where she sought refuge after the attack.
Local media cited neighbours as saying she suffered from mental illness.