Thanks to their lower losses and sharper resonances compared to their metallic counterparts, all-dielectric metasurfaces are attracting a quickly growing research interest. The application of such metasurfaces in the field of refractive index sensing is extremely attractive, especially due to the expected high performance and the simplicity of the sensing element excitation and readout. Herein, we report on an all-dielectric silicon metasurface based on complementary split-ring resonators (CSRRs) optimized for refractive index sensing. A quasi-bound state in the continuum (quasi-BIC) with an ultra-high quality factor can be excited in the near-infrared (NIR) window by violating the structure symmetry. By using the three-dimensional finite element method (3D-FEM), a refractive index sensor for biomedical applications with an ultra-high figure of merit (FoM > 100,000 RIU−1) has been designed, exploiting the quasi-BIC resonance. The proposed design strategy opens new avenues for developing flat biochemical sensors that are accurate and responsive in real time.