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In this paper, we propose a Fano-resonance-based refractive index sensor with ultra-high sensitivity. The sensor comprises a metal–insulator-metal (MIM) waveguide with two rectangular stubs coupled with a circular resonator embedded with a defective metal nanocube (CRMN). The transmission characteristics of the structure are simulated using the 2D finite element method. This analysis reveals that the Fano resonance mode splitting is affected by the geometry of the sensor. In addition, the modulation depth and position of the Fano resonance can be tuned by adjusting the width and length of the stub on the CRMN. Optimizing the structural parameters results in a peak sensing sensitivity of 10200 nm∙RIU−1 under the ultra-compact sensor size. This sensitivity allows the sensor to be used in the detection of hemoglobin concentration (HC). By processing simulation data, the linear relationship between the refractive index of three different blood groups (A, B, and O) and HC is obtained. Based on the sensing principle of the designed device, HC can be calculated from measuring the shift of the Fano resonance wavelength. These results provide critical developments for the application of nanoscale refractive index sensors in the biomedical field.