Background and Objectives: The recommended therapeutic management in renal cell carcinoma (RCC) with supradiaphragmatic inferior vena cava/right atrial thrombus (IVC/RA) is surgery. Extracorporeal circulation is required. Acute kidney injury (AKI), a frequent complication after nephrectomy and cardiac surgery is associated with long-term kidney disease. This study aims to identify the risk factors involved in the occurrence of the severe postoperative AKI (AKI3) and to analyse various preoperative validated risk scores from cardiac and noncardiac surgery in predicting this endpoint. Materials and Methods: The medical data of all patients with RCC with supradiaphragmatic IVC/RA thrombus who underwent radical nephrectomy with high thrombectomy, using extracorporeal circulation, between 2004–2018 in the Prof. C. C. Iliescu Emergency Institute for Cardiovascular Diseases, Bucharest, were retrospectively analysed. The patients who died intraoperatively were excluded from the study. The predefined study endpoint was the postoperative AKI3. Preoperative, intraoperative and postoperative data were collected according to the stratification of study population in two subgroups: AKI3-present and AKI3- absent patients. EuroSCORE, EuroSCORE II, Logistic EuroSCORE, NSQIP any-complications and NSQIP serious-complications were analysed. Results: We reviewed 30 patients who underwent this complex surgery between 2004–2018 in our institute. Two patients died intraoperatively. Nine patients (32.14%) presented postoperative AKI3. Age (OR 1.151, CI 95%: 1.009–1.312), preoperative creatinine clearance (OR 1.066, CI 95%: 1.010–1.123) and intraoperative arterial hypotension (OR 13.125, CI 95%: 1.924–89.515) were risk factors for AKI3 (univariable analysis). Intraoperative arterial hypotension emerged as the only independent risk factor in multivariable analysis (OR 11.66, CI 95%: 1.400–97.190). Logistic EuroSCORE (ROC analysis: AUC = 0.813, p = 0.008, CI 95%: 0.633–0.993) best predicted the endpoint. Conclusions: An integrated team effort is essential to avoid intraoperative arterial hypotension, the only independent risk factor of AKI3 in this highly complex surgery. Some risk scores can predict this complication. Further studies are needed.