A promising design principle for reducing the carbon footprint of buildings is modular construction using reusable, thin-walled components made of carbon fiber-reinforced concrete. In the numerical analysis of such systems, the nonlinear simulation of different structural assemblies of the same substructures and different loading scenarios is computationally expensive. We present a component-wise reduced-order modeling (ROM) framework to efficiently simulate such modular systems, where the system-level reduced-order model is assembled from reduced-order models of the substructures. For each structural component, reduced-order models are constructed using Proper Orthogonal Decomposition (POD) and further accelerated through Energy-Conserving Sampling and Weighting (ECSW) to achieve hyper-reduction of the nonlinear governing equations. The reduced components are assembled at the system level using a mortar tied-contact formulation, allowing for non-matching meshes of substructures within the reduced framework. This enables efficient simulation of different assemblies without recomputing component-level reduced bases. The proposed approach is demonstrated on thin-walled CFRC modular structures under quasi-static loading. The framework captures geometrically nonlinear behavior and inelastic material response modeled through plasticity, while significantly reducing computational effort compared to full-order models. Numerical results show good agreement in global and local response quantities across multiple assembly configurations.