Redox flow batteries (RFBs) have emerged as a promising option for large-scale energy storage, owing to their high energy density, low cost, and environmental benefits. However, the identification of organic compounds with high redox activity, aqueous solubility, stability, and fast redox kinetics is a crucial and challenging step in developing an RFB technology. Density functional theory-based computational materials prediction and screening is a time-consuming and computationally expensive technique, yet it has a high success rate. To speed up the discovery of new materials with desired properties, machine-learning-based models can be trained on large data sets. Graph neural networks (GNNs) are particularly well-suited for non-Euclidean data and can model complex relationships, making them ideal for accelerating the discovery of novel materials. In this study, a GNN-based model called MolGAT was developed to predict the redox potential of organic molecules using molecular structures, atomic properties, and bond attributes. The model was trained on a data set of over 15,000 compounds with redox potentials ranging from −4.11 to 2.56. MolGAT outperformed other GNN variants, such as the Graph Attention Network, Graph Convolution Network, and AttentiveFP models. The trained model was used to screen a vast chemical data set comprising 581,014 molecules, namely OMDB, QM9, ZINC, CHEMBL, and DELANEY, and identified 23,467 potential redox-active compounds for use in redox flow batteries. Of those, 20,716 molecules were identified as potential catholytes with predicted redox potentials up to 2.87 V, while 2,751 molecules were deemed potential anolytes with predicted redox potentials as low as −2.88 V. This work demonstrates the capabilities of graph neural networks in condensed matter physics and materials science to screen promising redox-active species for further electronic structure calculations and experimental testing.