Background: Acute kidney injury (AKI) is associated with substantial mortality. In this case–control study, we analyzed the impacts of AKI and chronic kidney disease (CKD) on outcomes in a group of 323 patients with severe COVID-19. The correlation of clinical and laboratory data with AKI and CKD was also analyzed. Methods: A retrospective case–control study was conducted among AKI, CKD, and normal kidney function (NKF) groups hospitalized in a COVID-19 center in 2021. Results: AKI patients had higher in-hospital mortality (55.2 vs. 18.8%, p < 0.001), more frequent transfers from the HDU to ICU (57.5 vs. 12.9%, p < 0.001), and prolonged hospital stays (15.4 ± 10.7 vs. 10.7 ± 6.7 days, p < 0.001) compared to the NKF group. AKI was a predictor of death (OR 4.794, 95%CI: 2.906–7.906, p < 0.001). AKI patients also had broader lung parenchymal involvement and higher inflammatory markers compared to the NKF group. Patients with prior CKD had higher in-hospital mortality compared to the NKF group (64.0 vs. 18.8%, p < 0.001, OR 4.044, 95%CI: 1.723–9.490, p = 0.013); however, transfers from the HDU to ICU were not more frequent (16.0 vs. 12.9%, p = 0.753). Conclusions: AKI among COVID-19 patients was correlated with more ICU transfers, higher morbidity, and greater markers of severe disease. Patients with CKD had a higher mortality; however, the rate of ICU transfer was not substantially higher due to their poor prognosis.