The application of fiber Bragg grating (FBG) sensors in the Internet of Things (IoT) has attracted wide attention for promising scenarios, such as remote monitoring of the subsidence of transformer substations, intelligent sensing of the power grid, and monitoring the safety of mines. However, disaster prewarning and forecasting in infrastructure construction require the key technology of remote sensing and monitoring. To resolve the current problems existing in monitoring the subsidence of substations built on a slope, an inclinometer based on FBG sensor technology is developed in this study. The FBG inclinometer sensor includes a rigid unit, a flexible sensing unit, and a connecting pin shaft. The flexible sensing unit is equipped with an FBG beam structure with uniform strength. The designed FBG is arranged symmetrically on the surface of the beam structure to eliminate the influence of temperature on measurement. In addition, a system that uses the FBG inclinometer sensor for remotely monitoring the subsidence of a transformer substation is designed. This system can display the subsidence of the substation on-site or at a remote terminal in real time. Indoor and field tests are carried out on the remote monitoring system. The test results show that the minimum resolution of the system is 0.1 mm and the maximum measurement error is less than 3%, which meet the requirements of on-site use.