Knowledge graphs (KGs) have great potential in various practical applications, especially in education. Educational KGs are of major importance in course design and personal learning. They collected and integrated data from multiple sources, such as textbooks and education guidelines, to provide systematic knowledge architecture for learners, gradually improving education quality. Previous work focused on massive manual operations and professional knowledge to build KGs and presented many limitations, such as increased time consumption. To address the above issues, this study proposes a pipeline that combines large language models (LLMs) and a graph embedding method to support KG construction for medical informatics, LLM-MIKG. Specifically, the entire construction process can be divided into three critical phases. First, we adopt a top-down approach to create an ontology, dividing medical informatics into clinical informatics, bioinformatics, pharmaceutical informatics, medical intelligence, medical information security, and intelligent medicine. Second, the prompting engineering should be optimized. This study designs a recursive prompting strategy to extract the entities and relationships of each knowledge node from top to bottom, forming many local KGs. Then, a graph embedding method is used to fuse local KGs to merge duplicate entities, establishing a complete medical informatics KG. Finally, the experimental results demonstrated the superiority of the proposed pipeline. We visualized 30,000 nodes on neo4j and deployed it on a self-developed medical informatics lifelong education platform to support further educational applications, which is an innovative attempt at medical informatics.