The hospital reported the case to police and the baby has been removed from his parents.
Doctors believe the child's calcium level may have exacerbated a heart condition, which caused him to undergo emergency surgery.
“This forces us to reflect on uncommon feeding regimes, even if in this case it was complicated by a cardiac malformation,” Luca Bernardo, director of pediatrics at the hospital the baby was brought to, told The Telegraph.
“It is not a problem to choose different or unusual kinds of nutrition and we certainly do not want to enter into a discussion of the merits of the decision," Bernardo said. "But since birth, the baby should have had support in this case with calcium and iron.”
The National Health Service says that it is important that babies breastfeeding from a vegan parent have Vitamin D and Vitamin B12, which may mean mothers need to take a supplement.
The baby is recovering well from surgery.
A Milan court ruled the child will remain in custody of the hospital as the investigation continues. The children's court will determine if the baby will be in the custody of the grandparents, who brought him to the hospital.