(1) Background: SARS-CoV-2 infection during pregnancy could determine important maternal and fetal complications. We aimed to prospectively assess placental immunohistochemical changes, immunophenotyping alterations, and pregnancy outcomes in a cohort of patients with COVID-19; (2) Methods: 52 pregnant patients admitted to a tertiary maternity center between October 2020 and November 2021 were segregated into two equal groups, depending on the presence of SARS-CoV-2 infection. Blood samples, fragments of umbilical cord, amniotic membranes, and placental along with clinical data were collected. Descriptive statistics and a conditional logistic regression model were used for data analysis; (3) Results: Adverse pregnancy outcomes such as preterm labor and neonatal intensive care unit admission did not significantly differ between groups. The immunophenotyping analysis indicated that patients with moderate–severe forms of COVID-19 had a significantly reduced population of T lymphocytes, CD4+ T cells, CD8+ T cells (only numeric), CD4+/CD8+ index, B lymphocytes, and natural killer (NK) cells. Our immunohistochemistry analysis of tissue samples failed to demonstrate positivity for CD19, CD3, CD4, CD8, and CD56 markers; (4) Conclusions: Immunophenotyping analysis could be useful for risk stratification of pregnant patients, while further studies are needed to determine the extent of immunological decidual response in patients with various forms of COVID-19.