In Intensive Care Units (ICUs), sepsis-induced Acute Kidney Injury (AKI) is a life-threatening complication associated with high mortality and long-term morbidity. Sequential Organ Failure Assessment (SOFA) score, like other traditional screening tools is often calculated infrequently and fails to capture the complex, time-varying interplay between physiological systems that precedes organ failure. This study introduces a Dynamic Graph Neural Network (DGNN) approach to model the evolving relationships among physiological variables for the early and accurate prediction of sepsis-induced AKI. Unlike traditional time-series models, the DGNN represents each physiological variable such as Heart Rate (HR), lactate, creatinine, vasopressor dose as a node. This dynamically learn the weighted edges that capture the evolving patient pathophysiology at each time step. The DGNN was trained using multivariate time-series extracted from a cohort of adult septic IC patients within the Medical Information Mart for Intensive Care IV (MIMIC-IV) database. The model was tasked with predicting the onset of AKI (Kidney Disease Improving Global Outcomes (KDIGO) criteria) within 6, 12, 24, and 36-hour prediction windows, benchmarked against the static SOFA score and an established deep learning model, the Long Short-Time Memory (LSTM) network. The experimental results show the supremacy in the performance of DGNN across all time horizons. For critical 12-hour prediction window, the model achieved an Area Under the Receiver Operating Characteristic (AUROCs) of 0.89, significantly outperforming LSTM (0.82) and baseline SOFA (0.71). Furthermore, DGNN maintains a robust Area Under the Receiver (AUC) of 0.80 for the 36-hour window, thus provides a much earlier warning than the current methods. Analysis of the learned graph edges revealed clinically relevant insights, such as the increasing influence of vasopressor dose and rising lactate on renal function markers preceding AKI onset. This model offers a more robust and accurate early warning system, reflecting the systemic nature of sepsis and holding significant potential to facilitate timely interventions and improve patient outcomes.