The four-year-old brother of the baby Irfan Ahmed has also sustained injury during the attack.
Police said that protesters, who were calling for a shutdown in Baramulla, intercepted the vehicle in which the family was traveling to take Irfan for treatment.
Despite the family's plea that the baby needed immediate medical attention, the mob refused to let them go and started attacking the vehicle.
"Some people came in Tata Sumos and were throwing stones. They got into our vehicle, they hit the 10-day-old baby who was in his mother's lap. They were protesting and hit my other son in the head. He is only three years old. My 10-day-old was hit and pushed to the window. Blood poured out of his nose. We took him to hospital where he was declared brought dead," the grieving father said in a TV news report.
Reacting to the killing, Chief Minister Omar Abdullah, while criticizing the opposition for supporting the mob, has promised the family of immediate action.