Nowadays, healthcare has become an important area for the Internet of Things (IoT) to automate healthcare facilities to share and use patient data anytime and anywhere with Internet services. At present, the host-based Internet paradigm is used for sharing and accessing healthcare-related data. However, due to the location-dependent nature, it suffers from latency, mobility, and security. For this purpose, Named Data Networking (NDN) has been recommended as the future Internet paradigm to cover the shortcomings of the traditional host-based Internet paradigm. Unfortunately, the novel breed lacks a secure framework for healthcare. This article constructs an NDN-Based Internet of Medical Things (NDN-IoMT) framework using a lightweight certificateless (CLC) signature. We adopt the Hyperelliptic Curve Cryptosystem (HCC) to reduce cost, which provides strong security using a smaller key size compared to Elliptic Curve Cryptosystem (ECC). Furthermore, we validate the safety of the proposed scheme through AVISPA. For cost-efficiency, we compare the designed scheme with relevant certificateless signature schemes. The final result shows that our proposed scheme uses minimal network resources. Lastly, we deploy the given framework on NDN-IoMT.