Graph-based learning provides a powerful framework for modeling complex relational structures; however, its application within the domain of wireless security remains significantly underexplored. In this work, we introduce the first application of graph-based learning for jamming source localization, addressing the imminent threat of jamming attacks in wireless networks. Unlike geometric optimization techniques that struggle under environmental uncertainties and dense interference, we reformulate the localization as an inductive graph regression task. Our approach integrates structured node representations that encode local and global signal aggregation, ensuring spatial coherence and adaptive signal fusion. To enhance robustness, we incorporate an attention-based \ac{GNN} that adaptively refines neighborhood influence and introduces a confidence-guided estimation mechanism that dynamically balances learned predictions with domain-informed priors. We evaluate our approach under complex \ac{RF} environments with various sampling densities, network topologies, jammer characteristics, and signal propagation conditions, conducting comprehensive ablation studies on graph construction, feature selection, and pooling strategies. Results demonstrate that our novel graph-based learning framework significantly outperforms established localization baselines, particularly in challenging scenarios with sparse and obfuscated signal information. Our code is available at https://github.com/tiiuae/gnn-jamming-source-localization.