A high-finesse, optical fiber, extrinsic Fabry–Perot interferometric (EFPI) pressure sensor based on a microelectromechanical system (MEMS) technique is proposed and experimentally demonstrated. The essential element in the pressure sensor is the high-finesse EFPI cavity that consists of a Pyrex glass wafer, a micromachined silicon wafer, and highly reflective dielectric films. Another Pyrex glass is used for fixing an optical fiber collimator, which allows the realization of the alignment of the incident light. Experimental results show that the proposed sensor exhibits a pressure sensitivity of 1.598 μm/MPa and a high-pressure sensing resolution of 0.002% of the full scale. This sensor is expected to benefit many applications that require high-accuracy pressure measurements, and especially atmospheric pressure applications.