In this paper, we propose a novel distributed fault detection method to monitor the state of a-possibly large scale-linear system, partitioned into interconnected subsystems. The approach hinges on the definition of a partition-based distributed Luenberger-like estimator, based on the local model of the subsystems and that takes into account their dynamic coupling. The proposed methodology computes-in a distributed way-a bound on the variance of a properly defined residual signal. This bound depends on the uncertainty affecting the state estimates computed by the neighboring subsystems and it allows the computation of local fault detection thresholds, as well as the maximum false-alarm rate. The implementation of the proposed estimation and fault detection method is scalable, allowing Plug & Play operations, and the possibility to disconnect the faulty subsystem after fault detection. Theoretical conditions on the convergence properties of the estimates and of the estimation error bounds are provided. Simulation results on a power network benchmark show the effectiveness of the proposed method.