The virus responsible for COVID-19 is designated “severe acute respiratory syndrome coronavirus 2” (SARS-CoV-2), a highly transmissible and pathogenic coronavirus. Although people of all ages are susceptible to SARS-CoV-2 infection, clinical manifestations may vary with age. The response of neonates to SARS-CoV-2 infection or exposure differs from that of children and adults. Encephalitis due to viral infections in the central nervous system (CNS) and childhood multisystem inflammatory syndrome (MIS-C) are some of the possible neonatal consequences of SARS-CoV-2 infection. This review aims to verify possible neonatal neurological outcomes after SARS-CoV-2 infection. Overall, the cellular and molecular basis of the neurological sequelae of SARS-CoV-2 in neonates remains unclear, and attempts to elucidate the pathophysiology of COVID-19 involve a comparison with the mechanism of other viral diseases. There are a considerable number of case reports in the literature exploring neurological outcomes in the neonatal period. In this review, we present possible effects of SARS-CoV-2 in neonates, emphasizing the importance of monitoring this group. The mechanisms of SARS-CoV-2 entry into the CNS have not yet been fully elucidated, and the potential severity of SARS-CoV-2 infection in neonates, as well as the possible short- and long-term neurological sequelae, remain unclear.