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Biomedical knowledge graphs (KGs) encode rich, structured information critical for drug discovery tasks, but extracting meaningful insights from large-scale KGs remains challenging due to their complex structure. Existing biomedical subgraph retrieval methods are tailored for graph neural networks (GNNs), limiting compatibility with other paradigms, including large language models (LLMs). We introduce K-Paths, a model-agnostic retrieval framework that extracts structured, diverse, and biologically meaningful multi-hop paths from dense biomedical KGs. These paths enable prediction of unobserved drug-drug and drug-disease interactions, including those involving entities not seen during training, thus supporting inductive reasoning. K-Paths is training-free and employs a diversity-aware adaptation of Yen's algorithm to extract the K shortest loopless paths between entities in a query, prioritizing biologically relevant and relationally diverse connections. These paths serve as concise, interpretable reasoning chains that can be directly integrated with LLMs or GNNs to improve generalization, accuracy, and enable explainable inference. Experiments on benchmark datasets show that K-Paths improves zero-shot reasoning across state-of-the-art LLMs. For instance, Tx-Gemma 27B improves by 19.8 and 4.0 F1 points on interaction severity prediction and drug repurposing tasks, respectively. Llama 70B achieves gains of 8.5 and 6.2 points on the same tasks. K-Paths also boosts the training efficiency of EmerGNN, a state-of-the-art GNN, by reducing the KG size by 90% while maintaining predictive performance. Beyond efficiency, K-Paths bridges the gap between KGs and LLMs, enabling scalable and explainable LLM-augmented scientific discovery. We release our code and the retrieved paths as a benchmark for inductive reasoning.