The growing interest in sustainability increases the challenges for decision makers in selecting the sustainable suppliers in which consider economic, environmental and social aspects. Particularly, decision makers are being increasingly motivated to improve their supply chain activities in coping efficiently with the objectives of sustainable development. Where the era of sustainability threatens the current supply chain partners to either cope with the new regulations of sustainability or leave the field for new players. Notwithstanding, most of the recent studies considered economic and green criteria in handling sustainable supplier selection and order allocation (SSS/OA) problems overlooking the social criteria which represents the third pillar of sustainability. This work aims at putting forward a hybrid Multi Criteria Decision-Making (MCDM)-Fuzzy Multi-Objective Optimization (FMOO) approach for a sustainable supplier selection and order allocation problem by considering economic, environmental and social criteria. Thus, an integrated Fuzzy AHP-Fuzzy TOPSIS is proposed to assess and rank suppliers according to three sets of criteria (i.e. conventional, green and social). A Multi-Objective Optimization Model (MOOM) is developed for choosing suppliers and allocating the optimal order quantities. To cope with the multiple uncertainties in the input data, the MOOM is reformulated into a Fuzzy Multi-Objective Optimization Model. The ε-constraint and LP-metrics approaches are used to reveal two sets of Pareto solutions based on the developed FMOO model. Finally, TOPSIS is applied to select the final Pareto solution that is closest to the ideal solution and furthest from the nadir solution. The effectiveness and the applicability of the developed hybrid MCDM-FMOO approach is demonstrated through a case study.