The SARS-CoV-2 virus emerged in December 2019 and then spread globally. Little is still known about the impact of COVID-19 on pregnant women and neonates. A review of the literature was performed according to the PRISMA guideline recommendations, searching the MEDLINE and EMBASE databases. Studies’ quality assessments were performed using the JBI Critical Appraisal Checklist. A total of 37 studies were included, involving 275 pregnant women with COVID-19 and 248 neonates. The majority of pregnant women presented with mild to moderate symptoms, only 10 were admitted in the ICU, and one died. Two stillbirths were reported and the incidence of prematurity was 28%. Sixteen neonates were tested positive for SARS-CoV-2 by RT-PCR, and nine of them were born from mothers infected during pregnancy. Neonatal outcomes were generally good: all the affected neonates recovered. RT-PCR for SARS-CoV-2 yielded negative results on amniotic fluid, vaginal/cervical fluids, placenta tissue, and breast milk samples. SARS-CoV-2 infection in pregnant women appeared associated with mild or moderate disease in most cases, with a low morbidity and mortality rate. The outcomes of neonates born from infected women were mainly favorable, although neonates at risk should be closely monitored. Further studies are needed to investigate the possibility of vertical transmission.