3D concrete printing (3DCP) enables formwork-free fabrication of complex cementitious structures. However, optimization of 3DCP remains challenging due to early age material behaviour and sensitivity to process parameters such as layer deposition rate and layer configuration. High-fidelity finite element simulations are commonly used to model layer deposition and time dependent material response, while reduced basis methods have been developed for nonlinear and nonaffine problems in solid mechanics. Nevertheless, reduced basis methods for real-time, parametric 3DCP simulations remain scarce. This contribution presents a projection-based intrusive reduced basis framework for efficient simulation of 3D concrete printing with nonlinear material behaviour. The approach is built upon a finite element formulation incorporating Drucker-Prager plasticity to represent the early age mechanical response of cementitious materials. To enable rapid evaluation across a multidimensional parameter space, a reduced basis is constructed from high-fidelity solution snapshots, and a Petrov-Galerkin projection strategy is employed for the reduced system. The computational cost associated with nonlinear constitutive evaluations is addressed through hyper-reduction techniques, allowing efficient approximation of internal force contributions while retaining accuracy in the presence of plasticity. The framework enables fast, real-time simulation of layer-by-layer deposition, capturing elastic-dominated early stages and nonlinear material effects in later layers, supporting simulation-driven design, parameter studies and optimization of 3D concrete printing.