This work presents the design and implementation of a data-driven Nonlinear Model Predictive Control (NMPC) framework for an Uncrewed Aerial Vehicle (UAV) equipped with a 3-DOF robotic arm. Real-world data was collected using the Matrice 100 platform and Dynamixel MX-28AR actuators to identify a high-dimensional linear model via Dynamic Mode Decomposition with Control (DMDc), capturing the interactions between the aerial vehicle and the manipulator across 21 state variables. This DMDc-based model is embedded within the NMPC formulation to predict system behavior over finite horizons. The UAV’s orientation is represented using quaternions, enabling continuous and singularity-free attitude control. Additionally, the redundancy of the UAV-manipulator system allows for the integration of secondary objectives into the cost function, supporting flexible task execution. To meet real-time requirements, the control problem is solved using the Acados solver. The resulting controller achieves high-precision tracking while managing internal constraints, demonstrating the potential of data-driven NMPC in aerial manipulation tasks