Detecting and localizing leakages is a significant challenge for the efficient and sustainable management of water distribution networks (WDN). Given the extensive number of pipes and junctions in real-world WDNs, full observation of the network with sensors is infeasible. Consequently, models must detect and localize leakages with limited sensor coverage. Leveraging the inherent graph structure of WDNs, recent approaches have used graph interpolation-based data-driven methods and graph neural network models (GNNs) for leakage detection and localization. However, these methods have a major limitation: data-driven methods often learn shortcuts that work well with in-distribution data but fail to generalize to out-of-distribution data. To address this limitation and inspired by the perfect generalization ability of classical algorithms, we propose an algorithm-informed graph neural network (AIGNN) for leakage detection and localization in WDNs. Recognizing that WDNs function as flow networks, incorporating max-flow information can be beneficial for inferring pressures. In the proposed framework, we first train AIGNN to emulate the Ford-Fulkerson algorithm, which is designed for solving max-flow problems. This algorithmic knowledge is then transferred to address the pressure estimation problem in WDNs. Specifically, two AIGNNs are deployed, one to reconstruct pressure based on the current measurements, and another to predict pressure based on previous measurements. Leakages are detected and localized by analyzing the discrepancies between the outputs of the reconstructor and the predictor. By pretraining AIGNNs to reason like algorithms, they are expected to extract more task-relevant and generalizable features. To the best of our knowledge, this is the first work that applies algorithmic reasoning to engineering applications. Experimental results demonstrate that the proposed algorithm-informed approach achieves superior results with better generalization ability compared to GNNs that do not incorporate algorithmic knowledge.