This article reports a multi-point curvature sensor system based on multiplexed optical fiber Fabry-Perot interferometric (FPI) sensor devices and a microwave photonics interrogation technique. The FPI sensor is fabricated with the assistance of a capillary tube, where a short section of the capillary is sandwiched between two single-mode fibers, forming the air-gap Fabry-Perot cavity. Bending of the FPI device leads to changes in the fringe contrast of its reflection spectrum. Based on the microwave photonics filtering technique, variations of the fringe contrast are encoded into the changes in the peak magnitude of the passband in the frequency response of the FPI device. By multiplexing such FPI devices with different cavity lengths, multi-point measurements of curvature can be realized by tracking changes in corresponding passbands in the frequency response of the system. The FPI curvature sensor is easy-to-manufacture and cost-effective, and the microwave photonics-based system provides an alternative and robust solution to interrogating the multiplexed FPI sensors for multi-point curvature sensing that could be desired in structural health monitoring, human-machine interface sensing, and other related fields.