Background Although diffuse alveolar damage and respiratory failure are the most common symptoms of coronavirus disease 2019, other organ involvement, such as the kidney, has been reported. The incidence of acute kidney injury in COVID-19 patients has been reported to vary greatly. In this study, we look at the magnitude and risk factors for acute kidney injury in COVID-19 patients in Ethiopia, a developing country. Methods A hospital-based retrospective cross-sectional study design was conducted among admitted COVID-19 patients at Eka Kotebe general hospital and Saint Peter COVID-19 treatment center by reviewing data from September 2020 to September 2021. A random sampling technique with proportional size allocation was used to select a total sample of 402 patients (225 from Eka Kotebe and 177 from St. Peter). Secondary data was collected from patient medical records using a standard, pre-tested data collection checklist using the Kobo toolbox, which was then exported to SPSS version 25.0 for analysis. The association between dependent and independent variables was analyzed using binary logistic regression. A statistical significance test was declared at a p value of <=0.05 with a 95% confidence interval. Results A total of 402 patient charts were reviewed, and the proportion of patients with acute kidney injury was found to be 18.9%. After adjusting for potential confounders, age<=35 years (AOR = 0.23, 95% CI = 0.07–0.72), female gender (AOR = 0.51, 95% CI = 0.28–0.94), and isolation type ICU (AOR = 5.11, 95% CI = 1.44–18.06) were significantly associated with acute kidney injury. Conclusion Acute kidney injury is a common complication in hospitalized COVID-19 patients. The prevalence of acute kidney injury in this study was 18.9%. Age, gender, and type of isolation were the factors that had a significant association with acute kidney injury. Clinicians and other concerned parties should provide more care to ICU patients and COVID-19 patients who are older.