Prefabricated building is an efficient building mode. Compared with the traditional building mode, the prefabricated building has advantages of less pollution, high construction efficiency, being more labor-saving, and economy, which is in line with China’s sustainable development strategy. This paper proposes a supplier selection evaluation model based on the mechanism equation model (SEM) and intuitionistic fuzzy analytic hierarchy process (IFAHP). Based on a detailed literature review, 300 structured questionnaires were distributed to the relevant enterprises, and an evaluation index system of prefabricated building element suppliers was built. With the fitting and modification process using a structural equation model, and assist of a path factor, an evaluation index system for evaluating the prefabricated building element suppliers was finally obtained. Finally, the intuitionistic fuzzy analytic hierarchy process was used to establish a selection model of prefabricated element suppliers, and the prefabricated element suppliers of Shuangyashan prefabricated construction projects were analyzed as a case study. The results show that the following factors have the most significant impact on supplier selection (from high to low): quality, economy, long-term cooperation, after-sales, and transportation. This study had a comprehensive consideration of the influencing factors existing in the whole selection process and should provide a valuable reference for the sustainable development of prefabricated construction engineering.