We report a simple Fabry-Perot interferometer (FPI) embedded in a glass chip, which is capable of precisely measuring the refractive indices of liquid samples. The microdevice is the integration of a single-mode optical fiber and a microchannel in the photosensitive glass fabricated by femtosecond laser followed by thermal treatment, wet etching, and annealing. The function of the FPI is demonstrated by measuring the refractive indices of water and methanol. The interference visibility is more than 4.0 dB, which is sufficient for most sensing applications. This refractive index sensor with rigid structure could be further integrated to become a more complex 3D lab-on-a-chip for reliable biomedical applications.