Along with the increasing interest in the metaverse as a new space for social interaction, privacy challenges that arise from new forms of data collection and usage have received notable research interest. Still, researchers and practitioners lack a structured overview of these privacy challenges as a foundation to explore measures that allow for safe and protected interaction in an ethical metaverse. To bridge this gap, we conducted a systematic literature review. We find that interaction in the metaverse carries the risk of revealing more sensitive personal data than in the traditional Internet. Moreover, we identify metaverse privacy challenges on different stakeholder levels, which often mirror those from the traditional Internet. Nevertheless, the metaverse also introduces novel facets to existing challenges due to its unique characteristics. These facets are discussed across six essential dimensions of privacy. Based on our findings, we provide recommendations for building a safe and secure metaverse environment.