This paper introduces a pioneering framework for music representation learning, which harnesses knowledge graph embeddings to enrich genre classification. Leveraging metadata from publicly available datasets like FMA and OpenMIC-2018, the constructed knowledge graph delineates intricate relationships among genres, artists, and instruments, offering valuable insights for genre representation. Within this framework, we propose two models tailored for distinct genre classification scenarios: fixed-set genre classification and open-set genre classification. These models exploit the knowledge graph to unveil correlations among different genres and integrate this knowledge into the audio representation. Notably, our approach is the first to merge audio data with high-level knowledge for music genre classification. Experimental results demonstrate that our proposed methods outperform state-of-the-art approaches, achieving an average genre classification accuracy of 68.07% on the FMA-medium dataset and 42.4% for open-set classification on the FMA-large dataset.