In recent years, the Internet of Medical Things (IoMT) is expanding its value as a key enabling technology for smart medical cyber-physical systems. In order to overcome the constraints of constrained local resources, smart medical equipment (ME) in IoMT cyber-physical systems offload data to edge or cloud servers for processing. However, due to the limited edge resources and huge time delay caused by offloading data to the cloud, the lack of a reasonable task unloading scheme will lead to the unbearable time delay and energy consumption of the IoMT system, resulting in uneven workloads among edge servers and threatening the security of medical data. To cope with these challenges, a deep deterministic policy gradient (DDPG)-based task-offloading method assisted by clustering is proposed. We first improved the initialization process of <italic>K</italic>-means, and based on this, designed an optimized <italic>K</italic>-means algorithm to carry out scientific and reasonable clustering of MEs according to their quality-of-service requirements. Then, DDPG is employed to obtain an optimal task-offloading scheme to minimize average latency and total energy consumption of IoMT and to ensure load balancing among edge servers. Finally, experimental results justify the scientific nature of optimized <italic>K</italic>-means and the superiority of DDPG in reducing the system overhead of IoMT. Compared with benchmark algorithms, DDPG reduces average time delay and total energy consumption by at least 16.9<inline-formula><tex-math notation="LaTeX">$&#x0025;$</tex-math></inline-formula> and 12.3<inline-formula><tex-math notation="LaTeX">$&#x0025;$</tex-math></inline-formula>, respectively.