Machine learning models deployed in critical care settings exhibit demographic biases, particularly gender disparities, that undermine clinical trust and equitable treatment. This paper introduces FairMed-XGB, a novel framework that systematically detects and mitigates gender-based prediction bias while preserving model performance and transparency. The framework integrates a fairness-aware loss function combining Statistical Parity Difference, Theil Index, and Wasserstein Distance, jointly optimised via Bayesian Search into an XGBoost classifier. Post-mitigation evaluation on seven clinically distinct cohorts derived from the MIMIC-IV-ED and eICU databases demonstrates substantial bias reduction: Statistical Parity Difference decreases by 40 to 51 percent on MIMIC-IV-ED and 10 to 19 percent on eICU; Theil Index collapses by four to five orders of magnitude to near-zero values; Wasserstein Distance is reduced by 20 to 72 percent. These gains are achieved with negligible degradation in predictive accuracy (AUC-ROC drop <0.02). SHAP-based explainability reveals that the framework diminishes reliance on gender-proxy features, providing clinicians with actionable insights into how and where bias is corrected. FairMed-XGB offers a robust, interpretable, and ethically aligned solution for equitable clinical decision-making, paving the way for trustworthy deployment of AI in high-stakes healthcare environments.