This paper presents a novel nanoscale refractive index sensor, which is produced by using a metal–insulator–metal (MIM) waveguide structure coupled with the circular ring with an external rectangular ring (CRERR) structure with the Fano resonance phenomenon. In this study, COMSOL software was used to model and simulate the structure, paired with an analysis of the output spectra to detail the effect of constructional factors on the output Fano curve as measured from a finite element method. After a series of studies, it was shown that an external rectangular ring is the linchpin of the unsymmetrical Fano resonance, while the circular ring’s radius strongly influences the transducer’s capability to achieve a maximum for 3180 nm/RIU sensitivity and a FOM of 54.8. The sensor is capable of achieving sensitivities of 0.495 nm/mgdL−1 and 0.6375 nm/mgdL−1 when detecting the concentration of the electrolyte sodium and potassium ions in human blood and is expected to play an important role in human health monitoring.