This work concerns with the inference of the Water Distribution Networks (WDN) state by using the smallest possible subset of sensor elements in order to aid the design of WDN monitoring systems. These nodes, which serve as network sensors, can be used to build a distributed monitoring system. First, we present the model in which we can represent the network structure as a linear discrete time invariant dynamical system. Using this model, we define the concept of network structural observability and present an efficient algorithm to minimize the cardinality of the subset of monitoring sensors. As a case study, we use simulation data generated with the well established EPANET simulator. Using the proposed method, we assess the estimation of nodes and link states. Also, we present the minimum number of sensors for various network simulation models found in the literature. To the best of our knowledge, this is the first work to use the proposed model to design general optimal water distribution network monitoring systems.