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The integration of Artificial Intelligence (AI) into the field of drug discovery has been a growing area of interdisciplinary scientific research. However, conventional AI models are heavily limited in handling complex biomedical structures (such as 2D or 3D protein and molecule structures) and providing interpretations for outputs, which hinders their practical application. As of late, Graph Machine Learning (GML) has gained considerable attention for its exceptional ability to model graph-structured biomedical data and investigate their properties and functional relationships. Despite extensive efforts, GML methods still suffer from several deficiencies, such as the limited ability to handle supervision sparsity and provide interpretability in learning and inference processes, and their ineffectiveness in utilising relevant domain knowledge. In response, recent studies have proposed integrating external biomedical knowledge into the GML pipeline to realise more precise and interpretable drug discovery with limited training instances. However, a systematic definition for this burgeoning research direction is yet to be established. This survey presents a comprehensive overview of long-standing drug discovery principles, provides the foundational concepts and cutting-edge techniques for graph-structured data and knowledge databases, and formally summarises Knowledge-augmented Graph Machine Learning (KaGML) for drug discovery. we propose a thorough review of related KaGML works, collected following a carefully designed search methodology, and organise them into four categories following a novel-defined taxonomy. To facilitate research in this promptly emerging field, we also share collected practical resources that are valuable for intelligent drug discovery and provide an in-depth discussion of the potential avenues for future advancements.