Over the past decade, wearable medical devices (WMDs) have become the norm for continuous health monitoring, enabling real-time vital sign analysis and preventive healthcare. These battery-powered devices face computational power, size, and energy resource constraints. Traditionally, low-power microcontrollers (MCUs) and application-specific integrated circuits (ASICs) have been used for their energy efficiency. However, the increasing demand for multi-modal sensors and artificial intelligence (AI) requires more computational power than MCUs, and rapidly evolving AI asks for more flexibility, which ASICs lack. Field-programmable gate arrays (FPGAs), which are more efficient than MCUs and more flexible than ASICs, offer a potential solution when optimized for energy consumption. By combining real-time reconfigurability with intelligent energy optimization strategies, FPGAs can provide energy-efficient solutions for handling multimodal sensors and evolving AI requirements. This paper reviews low-power strategies toward FPGA-based WMD for physiological monitoring. It examines low-power FPGA families, highlighting their potential in power-sensitive applications. Future research directions are suggested, including exploring underutilized optimizations like sleep mode, voltage scaling, partial reconfiguration, and compressed learning and investigating underexplored flash and hybrid-based FPGAs. Overall, it provides guidelines for designing energy-efficient FPGA-based WMDs.