Nowadays, sustainability within the chain of supply management has already become an issue of the current world economic realities, far more than in the context of Bangladesh garments industry. This paper develops a holistic approach to sustainable supplier selection, with a strong emphasis on a dimension that usually does not get the required attention — social responsibility. Intermingling Fuzzy AHP and DEMATEL into a hybrid approach for the same has rendered research on the selection of such a supplier, who balances economic performance with environmental and social considerations, complicated. The framework is structured; containment of expert judgments and multi-criteria decision analysis classify and evaluate suppliers with respect to environmental issues, social responsibility, operational factors, compliance, and economic factors. These results will give actionable insights to the practitioners in the garments sector to improve sustainable practices. This hybrid approach increases not only the robustness of supplier evaluation but also meets the growing demand that is growing globally for ethical supply chain standards.