Metaverse, the core of the next-generation Internet, is a computer-generated holographic digital environment that simultaneously combines spatio-temporal, immersive, real-time, sustainable, interoperable, and data-sensitive characteristics. It cleverly blends the virtual and real worlds, allowing users to create, communicate, and transact in virtual form. With the rapid development of emerging technologies including augmented reality, virtual reality and blockchain, the metaverse system is becoming more and more sophisticated and widely used in various fields such as social, tourism, industry and economy. However, the high level of interaction with the real world also means a huge risk of privacy leakage both for individuals and enterprises, which has hindered the wide deployment of metaverse. Then, it is inevitable to apply privacy computing techniques in the framework of metaverse, which is a current research hotspot. In this paper, we conduct comprehensive research on the necessity, taxonomy and challenges when privacy computing meets metaverse. Specifically, we first introduce the underlying technologies and various applications of metaverse, on which we analyze the challenges of data usage in metaverse, especially data privacy. Next, we review and summarize state-of-the-art solutions based on federated learning, differential privacy, homomorphic encryption, and zero-knowledge proofs for different privacy problems in metaverse. Finally, we show the current security and privacy challenges in the development of metaverse and provide open directions for building a well-established privacy-preserving metaverse system. For easy access and reference, we integrate the related publications and their codes into a GitHub repository: https://github.com/6lyc/Awesome-Privacy-Computing-in-Metaverse.git.