A supply chain (SC) is a network of interests, information, and materials involved in processes that produce value for customers. The implementation of blockchain technology in SC management in healthcare has had results. This review aims to summarize how blockchain technology has been used to address SC challenges in healthcare, specifically for drugs, medical devices (DMDs), and blood, organs, and tissues (BOTs). A systematic review was conducted by following the PRISMA guidelines and searching the PubMed and Proquest databases. English-language studies were included, while non-primary studies, as well as surveys, were excluded. After full-text assessment, 28 articles met the criteria for inclusion. Of these, 15 (54%) were classified as simulation studies, 12 (43%) were classified as theoretical, and only one was classified as a real case study. Most of the articles (n = 23, 82%) included the adoption of smart contracts. The findings of this systematic review indicated a significant but immature interest in the topic, with diverse ideas and methodologies, but without effective real-life applications.