False data injection attacks (FDIAs) represent a major class of attacks that aim to break the integrity of measurements by injecting false data into the smart metering devices in power grid. To the best of authors' knowledge, no study has attempted to design a detector that automatically models the underlying graph topology and spatially correlated measurement data of the smart grids to better detect cyber attacks. The contributions of this paper to detect and mitigate FDIAs are twofold. First, we present a generic, localized, and stealth (unobservable) attack generation methodology and a publicly accessible dataset for researchers to develop and test their algorithms. Second, we propose a Graph Neural Network (GNN) based, scalable and real-time detector of FDIAs that efficiently combines model-driven and data-driven approaches by incorporating the inherent physical connections of modern AC power grids and exploiting the spatial correlations of the measurement data. It is experimentally verified by comparing the proposed GNN based detector with the currently available FDIA detectors in literature that our algorithm outperforms the best available solutions by 6.21\%, 0.69\%, and 2.73\% in detection rate and by 3.65\%, 0.34\% and 1.38\% in F1 score for standard IEEE testbeds with 14, 118, and 300 buses, respectively.