Music-generative AI raises multiple challenges particularly related to the work of artists, the existing music industry model, the role of AI in creative processes, and the discussion of intellectual property rights. Our study addresses these challenges by examining transparency in music generation. We conduct a systematic literature review, following the PRISMA methodology, to gain a comprehensive understanding of the associations between algorithmic transparency, music generation, the evaluation in terms of creativity and originality, and the connections to intellectual property rights.We identify 1,111 publications by formulating four research questions. Following a rigorous review process, we narrow down the selection to 66 relevant investigations published by 2022, covering multiple AI domains. Acknowledging the rapid growth of the music generation field, we then incorporate 18 publications from 2023, focusing our search on the music-specific domain and novel applications. Thus, the present review overviews 84 publications. Our findings highlight a growing interest in AI transparency and the ethical consequences of generative models. However, transparent strategies in music-generative AI remain an under-explored topic. Our main contribution is the identification of research gaps and challenges in transparency for music-generative AI.