Zero Trust model enhances the security of wireless network environments, which is thought to be effectively applicable to Connected and automated vehicles (CAVs). Considering the abundance of real-time data in CAVs and the delay introduced by the data validation of the Zero Trust model, it may result in significant delay when processing real-time data. By caching popular content in advance on edge servers, edge caching can significantly reduce the response delay of real-time data in CAVs. However, achieving low-delay service responses requires ultra-dense deployments of edge servers, which increases the complexity of the wireless network. Therefore, it is challenging to achieve efficient cooperative caching between edge servers in Zero Trust-enabled CAVs. In this article, a Distributed Edge Caching method with Multi-Agent reinforcement learning for Zero Trust-enabled CAVs, named D-ECMA, is proposed. Specifically, a collaboration graph construction method is designed to obtain efficient collaborative relationships. Then a prediction method for the demand of services based on Spatial-Temporal Fusion Graph Neural Networks (STFGNN) is proposed to help edge servers adjust their caching policies. Following, a distributed edge caching method based on Multi-Agent Deep Deterministic Policy Gradient (MADDPG) for Zero Trust-enabled CAVs is designed. Finally, the effectiveness of D-ECMA is demonstrated through comparative experiments.