This paper aims to describe virtuous processes of social innovation (SI) management in the context of hospital care provision. It offers a revelatory case study concerning the Gaslini Research Hospital (Genoa), which has recently hired a managerial figure responsible for promoting SI projects. According to the best of the authors’ knowledge, this organization is the first Italian public hospital to incorporate such a role into its staff. The research investigates the primary features of this managerial position by analyzing the activities undertaken, institutional documents, and interviews with key informants. The collected data are analyzed using inductive reasoning and a system-wide perspective. The study highlights the contribution of the SI manager role in the hospital context, proposing a systems thinking model that identifies distributed leadership and organizational learning as enabling conditions for the implementation of social innovation, with implications useful for other healthcare institutions as well.