During pregnancy, SARS-CoV-2 infection is associated with several adverse outcomes, including an increased risk of pre-eclampsia, preterm delivery, hypertensive disorders, gestational diabetes, and fetal growth restriction related to the development of placenta vascular abnormalities. We analyzed human placenta from full-term, uncomplicated pregnancies with SARS-CoV-2 infection during the first, second, or third trimesters of gestation. We studied, by the immunohistochemistry technique, the expression of CD34 and podoplanin (PDPN) as markers of vasculogenesis to find any differences. As secondary outcomes, we correlated maternal symptoms with placental histological alterations, including fibrin deposits, lymphocyte infiltration in the villi, edema, and thrombi. Our results showed a PDPN expression around the villous stroma as a plexiform network around the villous nucleus of fetal vessels; significant down-regulation was observed in the villous stroma of women infected during the third trimester. CD34 showed no changes in expression levels. During SARS-CoV-2 infection, the most common maternal symptoms were fever, anosmia, ageusia and asthenia, and the majority were treated with paracetamol, corticosteroids and azithromycin. Patients that required multiple symptomatic treatments evidenced a large amount of fibrin deposition in the villi. Certainly, PDPN plays a key role in healthy placental vasculogenesis and thus in its proper physiology, and SARS-CoV-2 surely alters its normal expression. Further studies are necessary to understand what mechanisms are being altered to try to avoid possible complications for both the mother and fetus in terms of the contagions that will still occur.