Knowledge graphs (KGs) are important products of the semantic web, which are widely used in various application domains. Healthcare is one of such domains where KGs are intensively used, due to the high requirement for knowledge accuracy and interconnected nature of healthcare data. However, KGs storing general factual information often lack the ability to account for important contexts of the knowledge such as the status of specific patients, which are crucial in precision healthcare. Meanwhile, electronic health records (EHRs) provide rich personal data, including various diagnoses and medications, which provide natural contexts for general KGs. In this paper, we propose HypKG, a framework that integrates patient information from EHRs into KGs to generate contextualized knowledge representations for accurate healthcare predictions. Using advanced entity-linking techniques, we connect relevant knowledge from general KGs with patient information from EHRs, and then utilize a hypergraph model to “contextualize” the knowledge with the patient information. Finally, we employ hypergraph transformers guided by downstream prediction tasks to jointly learn proper contextualized representations for both KGs and patients, fully leveraging existing knowledge in KGs and patient contexts in EHRs. In experiments using a large biomedical KG and two real-world EHR datasets, HypKG demonstrates significant improvements in healthcare prediction tasks across multiple evaluation metrics. Additionally, by integrating external contexts, HypKG can learn to adjust the representations of entities and relations in KG, potentially improving the quality and real-world utility of knowledge.