This paper introduces a refractive index sensor based on Fano resonance, utilizing a metal–insulator–metal (MIM) waveguide structure with an Anchor-like cavity. This study utilizes the finite element method (FEM) for analyzing the propagation characteristics of the structure. The evaluation concentrated on assessing how the refractive index and the structure’s geometric parameters affect its sensing characteristics. The designed structure demonstrates optimum performance, achieving a maximum sensitivity of 2440 nm/RIU and an FOM of 63. Given its high sensitivity, this nanoscale refractive index sensor is ideal for detecting hemoglobin concentrations in blood, and the sensor’s sensitivity is 0.6 nm·g/L, aiding in clinical prevention and treatment.