The Internet of Medical Things (IoMT) is the network of medical devices, hardware infrastructure, and software applications used to connect the healthcare information technology. Massive traffic growth and user expectations cause challenges in the current exhausting models of IoMT data. To reduce the IoMT traffic, Information Centric Network (ICN) is a suitable technique. ICN uses persistent naming multicast communication that reduces the response time. ICN in IoMT provides a promising feature to reduce the overhead due to the distribution of commonly accessed contents. Some parameters such as energy consumption, communication cost, etc., influence the performance of sensors in the IoMT network. Excessive and unbalanced energy consumption degrades the network performance and lifetime. This article presents a framework called Dynamic Cache Scheme (DCS) that implements energy-efficient cache scheduling in IoMT over ICN to reduce network traffic. The proposed framework establishes a balance between the multi-hop traffic and data item freshness. The technique improves the freshness of data; thus, updated data are provided to the end-users via the effective utilization of caching in IoMT. The proposed framework is tested on important parameters, i.e., cache-hit-ratio, stretch, and content retrieval latency. The results obtained are compared with the state-of-the-art models. Results’ analysis shows that the proposed framework outperforms the compared models in terms of cache-hit-ratio, stretch, and content retrieval latency by 59.42%, 32.66%, and 18.8%, respectively. In the future, it is intended to explore the applicability of DCS in more scenarios and optimize further.