Healthcare is a binding domain for the Internet of Things (IoT) to automate healthcare services for sharing and accumulation patient records at anytime from anywhere through the Internet. The current IP-based Internet architecture suffers from latency, mobility, location dependency, and security. The Named Data Networking (NDN) has been projected as a future internet architecture to cope with the limitations of IP-based Internet. However, the NDN infrastructure does not have a secure framework for IoT healthcare information. In this paper, we proposed a secure NDN framework for IoT-enabled Healthcare (IoTEH). In the proposed work, we adopt the services of Identity-Based Signcryption (IBS) cryptography under the security hardness Hyperelliptic Curve Cryptosystem (HCC) to secure the IoTEH information in NDN. The HCC provides the corresponding level of security using minimal computational and communicational resources as compared to bilinear pairing and Elliptic Curve Cryptosystem (ECC). For the efficiency of the proposed scheme, we simulated the security of the proposed solution using Automated Validation of Internet Security Protocols and Applications (AVISPA). Besides, we deployed the proposed scheme on the IoTEH in NDN infrastructure and compared it with the recent IBS schemes in terms of computation and communication overheads. The simulation results showed the superiority and improvement of the proposed framework against contemporary related works.