Currently, the assessment of immune status in patients with COVID-19 is limited to determining the count of polymorphonuclear leukocytes and the phagocytic function of neutrophils, which is insufficient to understand the regulatory role of innate immunity cells in the development of pneumonia. However, no such studies have been conducted in pregnant women with COVID-19. The aim of this study was to investigate the functional state of neutrophil granulocytes in order to identify predictors of pneumonia severity risk in pregnant women with COVID-19. A clinical characterization of pregnant women with COVID-19 in addition to minimal and average lung changes was provided. The composition and ratio of morphological forms of leukocyte cells were studied. Cytochemical studies of neutrophil granulocytes were carried out and calculations of the mean cytological index (MCI) for succinate dehydrogenase, myeloperoxidase, and cationic proteins were performed. The number of NETs in blood smears was counted. Independent predictors of pneumonia severity in pregnant women with COVID-19 were calculated using regression analysis. The quality of the model was assessed using ROC analysis. In pregnant women with COVID-19 and an average volume of lung changes, the number of polymorphonuclear leukocytes (p = 0.03) and band neutrophils (p = 0.002) in the blood was significantly higher than in pregnant women with minimal lung changes. The MCI indicators of succinate dehydrogenase, cationic proteins, and myeloperoxidase in pregnant women with COVID-19 were reduced in relation to the control group (p < 0.0001). In blood smears of pregnant women with COVID-19 and an average volume of lung changes, the number of NETs increased (p = 0.002). Regression analysis showed that succinate dehydrogenase and NETs are independent predictors of pneumonia severity in pregnant women with COVID-19. Our study confirms the prognostic significance of low levels of neutrophilic succinate dehydrogenase and high levels of NETs in the blood of pregnant women with COVID-19. The combination of these two biomarkers is a significant reflection of the severity of pneumonia development in pregnant women with COVID-19. However, further research is needed to identify the mechanisms underlying this association.