Globally, increasing environmental issues are gaining attention to facilitate the adoption of green innovation for sustainable supply chain management (SSCM). Sustainable environmental practices have been well-considered in the literature; however, no study has focused on adopting green innovation practices for sustainable development. Thus, environmental management authorities are putting pressure on industries to implement green innovation criteria for SSCM operations. Moreover, it is important to select traditional suppliers to transform its practices to that of sustainable supply chains in order to achieve the industry’s sustainable supply chain goals. In response, this research identified and analyzed the green innovation criteria for SSCM and then selected a supplier that could implement green aspects in the SSCM. This study developed an integrated multi-criteria decision making (MCDM) model using the fuzzy analytical hierarchy process (FAHP) and the fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS). The objective of this study was to analyze suppliers to implement green innovation criteria for SSCM practices in the textile manufacturing companies of China. This study reviewed and identified three green innovation criteria and seventeen sub-criteria. Then, the FAHP technique was employed to analyze and rank green innovation criteria and sub-criteria. Finally, the FTOPSIS method was used to investigate and rank eight suppliers. The findings of the FAHP indicated that economic (EC) criteria were the most vital green innovation criteria in the SSCM. Furthermore, the FTOPSIS results revealed that supplier 5 was the most suitable supplier for implementing green innovation criteria in the SSCM. These findings will help managers, practitioners, and policymakers implement green innovation criteria in sustainable manufacturing supply chains.