The 22-week baby later died in an intensive care unit two days after the original abortion.
The case has caused controversy across the devoutly Roman Catholic country, with many questioning the legality of abortion.
The mother had opted for a termination after initial scans suggested that her baby would be born disabled.
The infant however survived the operation, carried out on Saturday at the Rossano Calabria hospital, before being left by doctors to die.
20 hours after the operation Father Antonion Martello, the hospital chaplain, discovered the boy was alive after praying by his body.
He found the baby, wrapped in a sheet with his umbilical cord still attached, was still moving.
The alarm was immediately raised and doctors organised for the boy to be taken to a specialist neo-natal unit at a nearby hospital. The boy died on Monday morning, some two days after the original termination.
The Italian government is considering an inquiry, while police are investigating the case for homicide, as the law in Italy states that doctors are obligated to assist children that survive a termination.
Eugenia Roccella, the under-secretary of state in the health department, stated: 'The minister of health will send inspectors to the hospital in Rossano Calabro to investigate what actually happened, and to see if the Law 194, which prohibits abortion when there is a possibility of the foetus living separately from the mother, and permits it only when the continuation of the pregnancy would result in life-threatening danger to the mother.'
She added that if initial reports were correct, 'this would be a case of deliberate abandonment of a seriously premature neonate, possibly also with some form of disability, an act contrary to any sense of human compassion but also of any accepted professional medical practice.'
She added: 'We must remember that a baby, once born, is an Italian citizen equal to all the others, and is entitled to all fundamental rights, including the right to health and therefore to be given full support.'
A spokesman for the British-based ProLife Alliance said: 'There cannot be anybody in the world who is not horrified by a story like this.'