We demonstrate a strain sensor with very high sensitivity in the static and low frequency regime based on a fiber ring cavity that includes a π phase-shifted fiber Bragg grating. The grating acts as a partial reflector that couples the two counter-propagating cavity modes, generating a splitting of the resonant frequencies. The presence of a sharp transition within the π phase-shifted fiber Bragg grating’s spectral transmittance makes this frequency splitting extremely sensitive to length, temperature, and the refractive index of the fiber in the region where the grating is written. The splitting variations caused by small mechanical deformations of the grating are tracked in real time by interrogating a cavity resonance with a locked-carrier scanning-sideband technique. The measurable strain range and bandwidth are characterized, and a resolution of 320 pϵ/Hz1/2 at 0 Hz is experimentally demonstrated, the highest achieved to date with a fiber Bragg grating sensor.