Recent advancements in Large language models (LLMs) have demonstrated remarkable capabilities across diverse domains. While they exhibit strong zero-shot performance on various tasks, LLMs' effectiveness in music-related applications remains limited due to the relatively small proportion of music-specific knowledge in their training data. To address this limitation, we propose MusT-RAG, a comprehensive framework based on Retrieval Augmented Generation (RAG) to adapt general-purpose LLMs for text-only music question answering (MQA) tasks. RAG is a technique that provides external knowledge to LLMs by retrieving relevant context information when generating answers to questions. To optimize RAG for the music domain, we (1) propose MusWikiDB, a music-specialized vector database for the retrieval stage, and (2) utilizes context information during both inference and fine-tuning processes to effectively transform general-purpose LLMs into music-specific models. Our experiment demonstrates that MusT-RAG significantly outperforms traditional fine-tuning approaches in enhancing LLMs' music domain adaptation capabilities, showing consistent improvements across both in-domain and out-of-domain MQA benchmarks. Additionally, our MusWikiDB proves substantially more effective than general Wikipedia corpora, delivering superior performance and computational efficiency.