Blockchain-based applications can enhance the sharing of information in processes involving multiple types of stakeholders, as in Supply Chain Management (SCM). A supply chain network can benefit from the visibility of the flow of goods, money, and information enabled by blockchain technology. So far, only limited evidence is available on the perspective of Small and Medium-sized Enterprises (SMEs) on the adoption of blockchain-based applications in their business processes. This may lead to a heavily diminished role for SMEs in SCM if large consortia unilaterally decide to adopt a blockchain-based architecture to improve the performance of the entire supply chain. Therefore, we conducted a study to explore which factors influence SMEs’ intention to adopt blockchain technology. Based on a literature review into technology adoption frameworks, we derived the technological, organizational, and environmental (TOE) factors that can play a role in their decision-making process. We distributed a survey amongst European SMEs using the multi-criteria decision-making method of the Best-Worst Method (BWM) to elicit the relative weights of these factors. The data analyses show that in contrast to other studies into technology adoption, the SMEs’ intention to adopt blockchain-based applications is primarily influenced by organizational rather than by technological and environmental factors. This implies that SMEs are best supported by showing blockchain’s organizational benefits and by training senior executives at their company.