False data injection attacks (FDIA) are a main category of cyber-attacks threatening the security of power systems. Contrary to the detection of these attacks, less attention has been paid to identifying the attacked units of the grid. To this end, this work jointly studies detecting and localizing the stealth FDIA in power grids. Exploiting the inherent graph topology of power systems as well as the spatial correlations of measurement data, this paper proposes an approach based on the graph neural network (GNN) to identify the presence and location of the FDIA. The proposed approach leverages the auto-regressive moving average (ARMA) type graph filters (GFs) which can better adapt to sharp changes in the spectral domain due to their rational type filter composition compared to the polynomial type GFs such as Chebyshev. To the best of our knowledge, this is the first work based on GNN that automatically detects and localizes FDIA in power systems. Extensive simulations and visualizations show that the proposed approach outperforms the available methods in both detection and localization of FDIA for different IEEE test systems. Thus, the targeted areas can be identified and preventive actions can be taken before the attack impacts the grid.