The concept of sustainability permeates every aspect of life and business. It is not only important to achieve economic goals, but also social and environmental ones. Besides other business fields, the concept of sustainability is also present within the supply chain. Selecting a green supplier that meets all sustainability requirements has become a paramount concern in today’s conditions. For that matter, this article proposes an integrated Multiple-Criteria Decision-Making (MCDM) approach based on the WENSLO (Weights by ENvelope and SLOpe) and WEDBA (Weighted Euclidean Distance-Based Approach) methods. The WENSLO method represents an objective weighting method used to define the significance of criteria, while the WEDBA method enables the definition of the optimal green supplier. The selection was based on criteria that encompassed all three aspects of sustainability: economic, social, and environmental. The proposed integrated approach was applied to a real case study, assessing the performance of five bottle suppliers for a beer factory. The results revealed that suppliers that better acknowledge the social and environmental requirements have somewhat weaker economic performances. Nevertheless, the integrated model facilitated the decision process and proved its applicability by providing reliable scientific results.