Edge computing as a disruptive solution addresses the emerging requirement of low latency data processing in Metaverse. However, edge computing resources are provided by computing service providers (ECPs) and thus it is essential to design appealing incentive mechanisms for the provision of limited resources. Meanwhile, deep learning (DL)-based auction has recently been proposed as an incentive mechanism that maximizes the revenue while holding important economic properties, i.e., individual rationality (IR) and incentive compatibility (IC). Therefore, in this work, we introduce the design of the DL-based auction for the computing resource allocation for the edge computing-assisted Metaverse. Furthermore, a semantic communication (SemCom) technique is exploited that helps to reduce the offloading data and offloading cost for the VSPs. Particularly, we briefly introduce the fundamentals and challenges of Metaverse. Second, we present edge computing, incentive mechanisms, and SemCom. Third, we present the design of the DL-based auction for edge resource allocation for the edge computing-assisted Metaverse. Simulation results demonstrate that the DL-based auction improves the revenue of the ECP and that VSPs pay a lower offloading cost with SemCom.