Modeling transient flow in networked dynamical systems characterized by hyperbolic partial differential equations (PDEs) is essential to engineering applications. Solutions of hyperbolic PDEs are commonly found using the method of characteristics (MOC), particularly when modeling the water hammer phenomenon in water distribution systems (WDSs), which is critical for design and operation. For applications that require fast modeling, existing methods for speeding up traditional MOC simulations either trade off accuracy for simulation time, or do not scale properly due to memory restrictions and prolonged computational times. This work proposes a novel parallel implementation of the MOC for networked systems, which relies on vectorization and distributed parallel computing to evaluate the transient dynamics of WDSs. The proposed method, referred to as distributed and vectorized MOC (DV‐MOC), relies on aligned memory allocation for vectorization and distributed‐memory parallelization to further accelerate vectorized operations and ensure scalability for arbitrary network topologies. The algorithm has been applied to a WDS from the battle of the sensor networks (BWSN‐II) composed by 14,824 pipes and nearly solution points. Through rigorous analyses, we show that the performance of DV‐MOC surpasses that of sequential MOC, with speeding up factors in the order of thousands for sufficiently dense numerical grids.