Background and Objectives: Kidney transplant recipients are at risk of developing more severe forms of COVID-19 infection. The aim of this study was to compare the clinical course of COVID-19 infection among kidney transplant patients and a control group. Materials and Methods: We examined 150 patients hospitalized with COVID-19 infection. Patients were divided into study (kidney transplant recipients, n = 53) and control (without a history of kidney transplantation, n = 97) groups. Demographics, clinical characteristics, treatment data, and clinical outcomes were assessed. Results: The median patient age was 56.0 (46.0–64.0) years, and seventy-seven patients (51.3%) were men. The median Charlson comorbidity index was higher in the study group (3.0 vs. 2.0, p < 0.001). There was a higher incidence of hypoxemia in the control group upon arrival (52.6% vs. 22.6%, p = 0.001) and a higher NEWS index median (2.0 vs. 1.0 points, p = 0.009) and incidence of pneumonia during hospitalization (88.7% vs. 73.6%, p = 0.023). In the study group, there were more cases of mild (26.4% vs. 11.3%, p = 0.023) and critically severe forms of COVID-19 infection (26.4% vs. 3.1%, p < 0.001), kidney failure was more prevalent (34.0% vs. 1.0%, p < 0.001), and a greater number of patients were transferred to the intensive care unit (22.6% vs. 3.1%, p < 0.001) and died (18.9% vs. 1.0%, p < 0.001). Multivariable analysis revealed that treatment in the intensive care unit correlated with a higher mortality rate than transplantation itself (HR = 20.71, 95% CI 2.01–213.33, p = 0.011). Conclusions: The course of the COVID-19 disease in kidney transplant recipients is heterogeneous and can be more severe than in the general population. Even though patients may be hospitalized with fewer symptoms, complications and death are more likely to occur.