Recent advances in edge computing and its imminent adoption in Sixth Generation (6G) wireless networks have led to a propitious paradigm defined as 6G edge computing. However, due to the communication mode and network virtualization of the 6G architecture, 6G edge computing presents several security concerns, including attack monitoring and detection. In this article, we present a new and robust Zero Trust Architecture (ZTA) empowered intrusion detection framework to protect 6G edge computing from network attacks. The proposed detection framework executes detection techniques based on security rules and machine learning algorithms as well as detection strategies based on a standalone and collaborative process with the goal to harden the security and hence to detect accurately the attacks. Furthermore, we propose a dynamic ZTA based on a non-cooperative game to harden further the security of 6G edge computing networks, with consideration of detection accuracy in terms of false positives and false negatives, and network cost as a computational overhead.