The original SARS-CoV-2 lineages have been replaced by successive variants of concern (VOCs) over time. The aim of this study was to perform an assessment of the placental infection by SARS-CoV-2 according to the predominant variant at the moment of COVID-19 diagnosis. This was a prospective study of SARS-CoV-2-positive pregnant women between March 2020 and March 2022. The population was divided into pregnancies affected by COVID-19 disease during 2020 (Pre-VOC group) and pregnancies affected after December 2020 by SARS-CoV-2 variants of concern (VOC group). The presence of virus was assessed by RT-PCR, and the viral variant was determined by whole genome sequencing. A total of 104 placentas were examined, among which 54 cases belonged to the Pre-VOC group and 50 cases belonged to the VOC group. Sixteen positive placental RT-PCR tests for SARS-CoV-2 were reported. The NGS analysis confirmed the SARS-CoV-2 lineage in placenta tissue. All samples corresponded to the Pre-VOC group, whereas no placental presence of SARS-CoV-2 was detected in the VOC group (16, 29.6% vs. 0, 0.0% p = 0.000). Preterm birth (9, 16.7% vs. 2, 4%; p = 0.036) and hypertensive disorders of pregnancy (14, 25.9% vs. 3, 6%; p = 0.003) were more frequent in the Pre-VOC group than in the VOC group. Finally, the VOC group was composed of 23 unvaccinated and 27 vaccinated pregnant women; no differences were observed in the sub-analysis focused on vaccination status. In summary, SARS-CoV-2-positive placentas were observed only in pregnancies infected by SARS-CoV-2 wildtype. Thus, placental SARS-CoV-2 presence could be influenced by SARS-CoV-2 variants, infection timing, or vaccination status. According to our data, the current risk of SARS-CoV-2 placental infection after maternal COVID disease during pregnancy should be updated.