Large Language Models (LLMs) have been driving progress in AI at an unprecedented rate, yet still face challenges in knowledge-intensive domains like biomedicine. Solutions such as pre-training and domain-specific fine-tuning add substantial computational overhead, and the latter require domain-expertise. External knowledge infusion is task-specific and requires model training. Here, we introduce a task-agnostic Knowledge Graph-based Retrieval Augmented Generation (KG-RAG) framework by leveraging the massive biomedical KG SPOKE with LLMs such as Llama-2-13b, GPT-3.5-Turbo and GPT-4, to generate meaningful biomedical text rooted in established knowledge. KG-RAG consistently enhanced the performance of LLMs across various prompt types, including one-hop and two-hop prompts, drug repurposing queries, biomedical true/false questions, and multiple-choice questions (MCQ). Notably, KG-RAG provides a remarkable 71% boost in the performance of the Llama-2 model on the challenging MCQ dataset, demonstrating the framework's capacity to empower open-source models with fewer parameters for domain-specific questions. Furthermore, KG-RAG enhanced the performance of proprietary GPT models, such as GPT-3.5 which exhibited improvement over GPT-4 in context utilization on MCQ data. Our approach was also able to address drug repurposing questions, returning meaningful repurposing suggestions. In summary, the proposed framework combines explicit and implicit knowledge of KG and LLM, respectively, in an optimized fashion, thus enhancing the adaptability of general-purpose LLMs to tackle domain-specific questions in a unified framework.