Coronavirus disease 2019 (COVID-19) requires admission to intensive care (ICU) for the management of acute respiratory distress syndrome in about 5% of cases. Although our understanding of COVID-19 is still incomplete, a growing body of evidence is indicating potential direct deleterious effects on the central and peripheral nervous systems. Indeed, complex and long-lasting physical, cognitive, and functional impairments have often been observed after COVID-19. Early (defined as during and immediately after ICU discharge) rehabilitative interventions are fundamental for reducing the neurological burden of a disease that already heavily affects lung function with pulmonary fibrosis as a possible long-term consequence. In addition, ameliorating neuromuscular weakness with early rehabilitation would improve the efficiency of respiratory function as respiratory muscle atrophy worsens lung capacity. This review briefly summarizes the polymorphic burden of COVID-19 and addresses possible early interventions that could minimize the neurological and systemic impact. In fact, the benefits of early multidisciplinary rehabilitation after an ICU stay have been shown to be advantageous in several clinical conditions making an early rehabilitative approach generalizable and desirable to physicians from a wide range of different specialties.