Biomedical knowledge graphs have emerged as powerful tools for drug discovery, but existing platforms often suffer from outdated information, limited accessibility, and insufficient integration of complex data. This study presents MedKG, a comprehensive and continuously updated knowledge graph designed to address these challenges in precision medicine and drug discovery. MedKG integrates data from 35 authoritative sources, encompassing 34 node types and 79 relationships. A Continuous Integration/Continuous Update pipeline ensures MedKG remains current, addressing a critical limitation of static knowledge bases. The integration of molecular embeddings enhances semantic analysis capabilities, bridging the gap between chemical structures and biological entities. To demonstrate MedKG's utility, a novel hybrid Relational Graph Convolutional Network for disease-drug link prediction, MedLINK was developed and used in case studies on clinical trial data for disease drug link prediction. Furthermore, a web-based application with user-friendly APIs and visualization tools was built, making MedKG accessible to both technical and non-technical users, which is freely available at http://pitools.niper.ac.in/medkg/.