The Internet of Medical Things (IoMT) has recently gained a lot of interest in the health care industry. IoMT enables real-time and omnipresent monitoring of a patient's health status, resulting in massive amounts of medical data being generated. The centralized massive data processing places enormous strain on the typical cloud computing, rendering it incapable of supporting a variety of real-time health care applications. Therefore, edge computing that moves application programs and data processing from central infrastructure to the edge nodes has attracted wide attention. However, adopting existing edge server (ES) deployment strategies for IoMT is not suitable due to the decentralized and high real-time service requirements of IoMT systems. In particular, traditional ES deployment strategies in IoMT system confront major load imbalance across ESs, latency issues, and energy consumption concerns. To address these challenges, a deployment strategy of ESs based on the state-action-reward-state-action (SARSA) learning, named ESL, is designed. Specifically, ESs are quantified by evaluating the silhouette coefficient (SC) and the sum of squared errors. Then, through fuzzy C-means (FCM) algorithm, the preliminary division of health monitoring units (HMUs) and the initial locations of ESs are obtained. Finally, SARSA learning is adopted to determine the deployment of ESs. Furthermore, extensive experiments and analyses confirm that ESL achieves the core objective of optimizing load balancing among ESs while also optimizing request-response latency and request processing energy consumption.