The construction sector accounts for a significant proportion of natural resource consumption and waste generation. This reveals the essentiality for gravitating the operations in the industry toward more sustainable paradigms. To tackle these concerns, the circular economy (CE) model has become a central concept to render conventional production and consumption behaviors in construction projects into innovative and sustainable patterns. In construction projects, selecting the most competent contractor is of paramount importance. Hence, the present research seeks to establish a comprehensive evaluation framework for sustainable circular contractor selection based on a hybrid fuzzy multicriteria decision-making (MCDM) approach. In this respect, the fuzzy analytical hierarchy process (AHP) was adopted for assessing the CE indicators, while the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) was utilized for evaluating circularity and eligibility of contractors. The utility of the proposed framework was predicated with regard to hydropower projects due to several environmental challenges encountered in the corresponding subsector. The results show that the contractors can be circular only if they have strong financial viability, develop strategies to implement ReSOLVE (regenerate, share, optimize, loop, virtualize, exchange), adopt specific construction methods to CE (e.g., modular construction), and propose sustainable innovative solutions. Overall, the proposed hybrid fuzzy MCDM framework can be used as a more systematic and transparent approach for selecting the most circular and sustainable contractors, contributing to the preservation of earth’s resources. Given the current contractors’ limited capacity to address circularity and sustainability concerns, the findings of this study can be regarded as a roadmap and contributes to practice by achieving circular and sustainable construction objectives with waste reduction, cost savings, and environmental benefits.