The four-month-old boy, identified as Giovannino, was diagnosed with harlequin ichthyosis, a rare genetic skin disorder in which babies are born with thick skin that cracks and splits apart.
The condition, which is said to affect just one person in every million, is the result of a faulty gene.
Present immediately at birth, the disorder can distort facial features and restrict breathing and eating, and requires intensive care.
Symptoms include tightness of the skin typically pulling around the eyes and mouth, forcing the eyelids and lips to turn inside out, and swollen hands and feet.
Infants born with harlequin ichthyosis are at an increased risk for low body temperature, dehydration and elevated levels of sodium in the blood.
They may also require tube feeding, and lubrication in the eyes to reduce the tightness of the eyelids.
Nurses at Sant’Anna hospital have been caring for Giovannino and say he is a happy little boy despite his condition.
“He is a cute child who smiles and loves being taken around the ward,” Daniele Farina, head of the hospital’s NICU, told Italian daily La Repubblica.
“He is happy when someone makes him listen to music.”
Nurses at the hospital are now trying to find a home for the baby.
The hospital has reportedly been inundated with offers to adopt Giovannino, and authorities are allegedly aware of the situation and looking for the parents.
The possibility of specialist foster care is also being considered.