Perinatal complications in both term- and preterm-born infants are a leading cause of neonatal morbidities and mortality. Infants face different challenges in the neonatal intensive care unit with long-term morbidities such as perinatal brain injury and bronchopulmonary dysplasia being particularly devastating. While advances in perinatal medicine have improved our understanding of the pathogenesis, effective therapies to prevent and/or reduce the severity of these disorders are still lacking. The potential of mesenchymal stem/stromal cell (MSC) therapy has emerged during the last two decades, and an increasing effort is conducted to address brain- and lung-related morbidities in neonates at risk. Various studies support the notion that MSCs have protective effects. MSCs are an easy source and may be readily available after birth in a clinical setting. MSCs' mechanisms of action are diverse, including migration and homing, release of growth factors and immunomodulation, and the potential to replace injured cells. Here, we review the pathophysiology of perinatally acquired brain and lung injuries and focus on MSCs as potential candidates for therapeutic strategies summarizing preclinical and clinical evidence.