Fast and accurate fault detection and localization in fiber optic cables is extremely important to ensure the optical network survivability and reliability. Hence there exists a crucial need to develop an automatic and reliable algorithm for real time optical fiber fault detection and diagnosis leveraging the telemetry data obtained by an optical time domain reflectometry (OTDR) instrument. In this paper, we propose a novel data driven approach based on convolutional neural networks (CNNs) to detect and characterize the fiber reflective faults given noisy simulated OTDR data, whose SNR (signal-to-noise ratio) values vary from 0 dB to 30 dB, incorporating reflective event patterns. In our simulations, we achieved a higher detection capability with low false alarm rate and greater localization accuracy even for low SNR values compared to conventionally employed techniques.