Fault detection is a topic of interest due to its importance to control and monitoring any kind of system. Generally, the most common failures occur in the actuators or the sensors. This article proposes using autoencoders to detect sensor faults in Continuous Glucose Monitoring (CGM) devices. The proposed methodology performs the task of detecting faults by the occurrence of disconnection, noise, and saturation in the sensors. Additionally, an optimization algorithm is applied to select the optimal threshold that discriminates if a fault occurs or not, which improves the accuracy. The results show that autoencoders are a powerful and versatile tool for fault detection, providing the distinction of faults with F1-scores of at least 86%.