The advances in deep learning (DL) techniques have the potential to deliver transformative technological breakthroughs to numerous complex tasks in modern power systems that suffer from increasing uncertainty and nonlinearity. However, the vulnerability of DL has yet to be thoroughly explored in power system tasks under various physical constraints. This work, for the first time, proposes a novel physics-constrained backdoor poisoning attack, which embeds the undetectable attack signal into the learned model and only performs the attack when it encounters the corresponding signal. The paper illustrates the proposed attack on the real-time fault line localization application. Furthermore, the simulation results on the 68-bus power system demonstrate that DL-based fault line localization methods are not robust to our proposed attack, indicating that backdoor poisoning attacks pose real threats to DL implementations in power systems. The proposed attack pipeline can be easily generalized to other power system tasks.