The ongoing Coronavirus disease 2019 (COVID-19) pandemic is disrupting most specialized healthcare services worldwide, including those for high-risk newborns and their families. Due to the risk of contagion, critically ill infants, relatives and professionals attending neonatal intensive care units (NICUs) are undergoing a profound remodeling of the organization and quality of care. In particular, mitigation strategies adopted to combat the COVID-19 pandemic may hinder the implementation of family-centered care within the NICU. This may put newborns at risk for several adverse effects, e.g., less weight gain, more nosocomial infections, increased length of NICU stay as well as long-term worse cognitive, emotional, and social development. This article aims to contribute to deepening the knowledge on the psychological impact of COVID-19 on parents and NICU staff members based on empirical data from the literature. We also provided evidence-based indications on how to safely empower families and support NICU staff facing such a threatening emergency, while preserving the crucial role of family-centered developmental care practices.