The Metaverse is a virtual environment where users are represented by avatars to navigate a virtual world, which has strong links with the physical one. State-of-the-art Metaverse architectures rely on a cloud-based approach for avatar physics emulation and graphics rendering computation. Such centralized design is unfavorable as it suffers from several drawbacks caused by the long latency required for cloud access, such as low quality visualization. To solve this issue, in this paper, we propose a Fog-Edge hybrid computing architecture for Metaverse applications that leverage an edge-enabled distributed computing paradigm, which makes use of edge devices computing power to fulfil the required computational cost for heavy tasks such as collision detection in virtual universe and computation of 3D physics in virtual simulation. The computational cost related to an entity in the Metaverse such as collision detection or physics emulation are performed at the end-device of the associated physical entity. To prove the effectiveness of the proposed architecture, we simulate a distributed social metaverse application. Simulation results shows that the proposed architecture can reduce the latency by 50\% when compared with the legacy cloud-based Metaverse applications.