This article presents a Galerkin projection-based reduced-order modeling (ROM) approach for segregated fluid–structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian–Eulerian (ALE) framework at low Reynolds numbers using the Finite Volume Method (FVM). The ROM is constructed using Proper Orthogonal Decomposition (POD) and incorporates a data-driven technique that combines classical Galerkin projection with radial basis function (RBF) networks. The results demonstrate the numerical stability and accuracy of the proposed method relative to the high-fidelity model.The ROM successfully captures transient flow fields and, importantly, the forces acting on the moving structure without exhibiting unphysical growth or divergence over time. This is further supported by the bounded evolution of error metrics and physical observables, which remain consistent with the full-order simulations throughout the prediction horizon. The method’s effectiveness is verified through a benchmark vortex-induced vibration (VIV) case involving a circular cylinder at Reynolds number . The hybrid ROM approach yields an accurate and efficient tool for solving FSI problems involving mesh motion.