Refractive index measurement is important for evaluation of liquid materials, optical components, and bio sensing. One promising approach for such measurement is use of optical fiber sensors such as surface plasmonic resonance or multi-mode interference (MMI), which measure the change of optical spectrum resulting from the refractive index change. However, the precision of refractive index measurement is limited by the performance of optical spectrum analyzer. If such the refractive index measurement can be performed in radio frequency (RF) region in place of optical region, the measurement precision will be further improved by the frequency-standard-based RF measurement. To this end, we focus on the disturbance-to-RF conversion in a fiber optical frequency comb (OFC) cavity. Since frequency spacing frep of OFC depends on an optical cavity length nL, frep sensitively reflects the external disturbance interacted with nL. Although we previously demonstrated the precise strain measurement based on the frep measurement, the measurable physical quantity is limited to strain or temperature, which directly interacts with the fiber cavity itself. If a functional fiber sensor can be installed into the fiber OFC cavity, the measurable physical quantity will be largely expanded. In this paper, we introduce a MMI fiber sensor into a ring-type fiber OFC cavity for refractive index measurement. We confirmed the refractive-index-dependent frep shift.