Music genres are shaped by both the stylistic features of songs and the cultural preferences of artists' audiences. Automatic classification of music genres using lyrics can be useful in several applications such as recommendation systems, playlist creation, and library organization. We present a multi-label, cross-lingual genre classification system based on multilingual sentence embeddings generated by sBERT. Using a bilingual Portuguese-English dataset with eight overlapping genres, we demonstrate the system's ability to train on lyrics in one language and predict genres in another. Our approach outperforms the baseline approach of translating lyrics and using a bag-of-words representation, improving the genrewise average F1-Score from 0.35 to 0.69. The classifier uses a one-vs-all architecture, enabling it to assign multiple genre labels to a single lyric. Experimental results reveal that dataset centralization notably improves cross-lingual performance. This approach offers a scalable solution for genre classification across underrepresented languages and cultural domains, advancing the capabilities of music information retrieval systems.