The growing popularity of social media platforms has sparked new marketing opportunities for companies. Marketers have turned to social media campaigns as a means to build brand loyalty, exposure, and engagement. While social media has evolved into a powerful marketing tool, marketers must carefully choose the most suitable social media platform. Improper selection of the social media platform can be costly and can be detrimental to the brand. Despite all of the supposed benefits, selecting the right social media platform has been a daunting task for corporate marketers. The social media platform selection problems are inherently complex problems with multiple and often conflicting criteria. We propose a novel analytical framework for social media platform selection. The proposed hybrid framework integrates the Analytic Network Process (ANP) with fuzzy set theory and the COmplex PRoportional ASsessment of alternatives with Grey relations (COPRAS-G) method. The ANP and fuzzy set theory are used to determine the importance weight of the social media platform selection criteria in a fuzzy environment. The COPRAS-G method is used to rank and select the most suitable social media platform. A case study is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.