Understanding excitonic effects in two-dimensional (2D) materials is critical for advancing their potential in next-generation electronic and photonic devices. In this study, we introduce a machine learning (ML)-based framework to predict exciton binding energies in 2D materials, offering a computationally efficient alternative to traditional methods such as many-body perturbation theory (GW) and the Bethe-Salpeter equation. Leveraging data from the Computational 2D Materials Database (C2DB), our ML models establish connections between cheaply available material descriptors and complex excitonic properties, significantly accelerating the screening process for materials with pronounced excitonic effects. Additionally, Bayesian optimization with Gaussian process regression was employed to efficiently filter materials with largest exciton binding energies, further enhancing the discovery process. Although developed for 2D systems, this approach is versatile and can be extended to three-dimensional materials, broadening its applicability in materials discovery.