The SARS-CoV-2 pandemic has imposed a huge challenge on the antenatal care of pregnant women worldwide, with the maternal mortality rate being raised to alarming levels. While COVID-19 vaccines were developed, some studies highlighted a possible relationship between influenza vaccination and lower odds of COVID-19 infection. As obstetric patients belong to a high-risk group for respiratory diseases, this study evaluated whether influenza vaccination reduces the severity of COVID-19 infection and mortality among pregnant and postpartum women. We conducted a retrospective cohort study on 3370 pregnant and postpartum women from the Brazilian national database, where they were grouped according to their influenza vaccination status before the onset of COVID-19 symptoms. The intensive care unit admission and intubation rates were significantly higher among subjects in the unvaccinated group (p = 0.002 and p < 0.001, respectively). The odds of mortality risk among those who received the vaccine was 0.33, with a 95% confidence interval of 0.23–0.47. The numbers of patients who needed to be vaccinated to avoid a case of intensive care unit admission, intubation, or death due to COVID-19 were 11, 15, and 11, respectively. Influenza vaccines could confer protection against severe COVID-19 infection in pregnant and postpartum women.