The recent advances in mobile devices and wireless communication sector transformed Mobile Augmented Reality (MAR) from science fiction to reality. Among the other MAR use cases, the incorporation of this MAR technology in the healthcare sector can elevate the quality of diagnosis and treatment for the patients. However, due to the highly sensitive nature of the data available in this process, it is also highly vulnerable to all types of security threats. In this paper, an edge-based secure architecture is presented for a MAR healthcare application. Based on the ESSMAR architecture, a secure key management scheme is proposed for both the registration and authentication phases. Then the security of the proposed scheme is validated using formal and informal verification methods.