Large language models (LLMs) have demonstrated significant potential in clinical decision support. Yet LLMs still suffer from hallucinations and lack fine-grained contextual medical knowledge, limiting their high-stake healthcare applications such as clinical diagnosis. Traditional retrieval-augmented generation (RAG) methods attempt to address these limitations but frequently retrieve sparse or irrelevant information, undermining prediction accuracy. We introduce KARE, a novel framework that integrates knowledge graph (KG) community-level retrieval with LLM reasoning to enhance healthcare predictions. KARE constructs a comprehensive multi-source KG by integrating biomedical databases, clinical literature, and LLM-generated insights, and organizes it using hierarchical graph community detection and summarization for precise and contextually relevant information retrieval. Our key innovations include: (1) a dense medical knowledge structuring approach enabling accurate retrieval of relevant information; (2) a dynamic knowledge retrieval mechanism that enriches patient contexts with focused, multi-faceted medical insights; and (3) a reasoning-enhanced prediction framework that leverages these enriched contexts to produce both accurate and interpretable clinical predictions. Extensive experiments demonstrate that KARE outperforms leading models by up to 10.8-15.0\% on MIMIC-III and 12.6-12.7\% on MIMIC-IV for mortality and readmission predictions. In addition to its impressive prediction accuracy, our framework leverages the reasoning capabilities of LLMs, enhancing the trustworthiness of clinical predictions.