In recent years, using wireless sensor networks (WSNs) for structural health monitoring (SHM) has attracted increasing attention. Traditional centralized SHM algorithms developed by civil engineers can achieve the highest damage detection quality since they have the raw data from all the sensor nodes. However, directly implementing these algorithms in a typical WSN is impractical considering the large amount of data transmissions and extensive computations required. Correspondingly, many SHM algorithms have been tailored for WSNs to become distributed and less complicated. However, the modified algorithms usually cannot achieve the same damage detection quality of the original centralized counterparts. In this paper, we select a classical SHM algorithm: the eigen-system realization algorithm (ERA), and propose a distributed version for WSNs. In this approach, the required computations in the ERA are updated incrementally along a path constructed from the deployed sensor nodes. This distributed version is able to achieve the same quality of the original ERA using much smaller wireless transmissions and computations. The efficacy of the proposed approach is demonstrated through both simulation and experiment.