The effect of SARS-CoV-2 infection on the pathophysiology of the placenta and its impact on pregnancy outcome has not yet been fully elucidated. Here, we present a comprehensive clinical, morphological, and molecular analysis of placental tissues from pregnant women with and without SARS-CoV-2 infection. SARS-CoV-2 could be detected in half of placental tissues from SARS-CoV-2-positive women. The presence of the virus was not associated with any distinctive pathological, maternal or neonatal outcome features. SARS-CoV-2 tissue load was low in all but one patient which exhibited severe placental damage leading to neonatal neurological manifestations. The placental transcriptional response induced by high viral load of SARS-CoV-2 showed an immunopathology phenotype similar to autopsy lung tissues from patients with severe COVID-19. This finding contrasted with the lack of inflammatory response in placental tissues from SARS-CoV-2-positive women with low viral tissue load and from SARS-CoV-2-negative women. Importantly, no evidence of vertical transmission of SARS-CoV-2 was found in any newborns, suggesting that the placenta may be an effective maternal-neonatal barrier against the virus even in the presence of severe infection. Our observations suggest that severe placental damage induced by the virus may be detrimental for the neonate independently of vertical transmission.