Objective Renal autoregulation, hemodynamic response, and endothelial dysfunction play significant roles in acute kidney injury (AKI) during perinatal asphyxia. A third mechanism of autoregulation, involving very low-frequency oscillations, has been described. This study aimed to evaluate the relationship between the power of the very low-frequency component of the Fast Fourier Transform (FFT) and AKI during therapeutic hypothermia (TH) treatment in neonates with perinatal asphyxia. Study design A retrospective longitudinal study was conducted on neonates with moderate and severe perinatal asphyxia. AKI was defined as a decrease of less than 33% in the serum creatinine level by day 3. The power of the very low-frequency component in the FFT was assessed by analyzing renal oxygen saturation using near-infrared spectroscopy (NIRS), focusing on a frequency band of approximately 0.01 Hz. Bivariate analyses were performed to explore the association between the power of the very-low-frequency component and AKI. The predictive ability of this component for AKI was evaluated using a receiver operating characteristic (ROC) curve. Additionally, a generalized estimating equation (GEE) was developed to investigate whether changes in the power of the very-low-frequency component during treatment differed according to the presence of AKI. Results A total of 91 patients were included in the study, of whom 15 (16.5%) developed AKI. Neonates with AKI exhibited a significantly lower power of the very low-frequency component on the second day of treatment ( p = 0.001). This component demonstrated good predictive ability for AKI (ROC curve 0.77, 95% CI 0.63–0.90). Conclusion Among neonates with perinatal asphyxia who developed AKI, a lower power of the very-low-frequency component in FFT (approximately 0.01 Hz) was observed on the second day of therapeutic hypothermia. This finding suggests that alterations in very-low-frequency oscillations may reflect endothelial dysfunction and contribute to the development of AKI, warranting further investigation in larger cohorts.