A novel model predictive attitude control method based on a Physics-informed Recurrent Neural Network (PI-RNN) is proposed for the attitude stabilization control problem of large-scale flexible space structures, which fully considers factors such as unknown vibration model parameters and unknown rigid-flexible coupling relationships. First, a PI-RNN predictive model for vibrations of flexible appendages is developed by embedding the prior physical vibration dynamics of large-scale flexible space structures into a Recurrent Neural Network (RNN), which facilitates accurate online prediction of the vibration modes of large-scale space structures. Then, the proposed PI-RNN predictive model is further integrated into a Nonlinear Model Predictive Control (NMPC) framework to overcome the problem that traditional NMPC methods are highly dependent on model accuracy. Moreover, the stability and feasibility of the closed-loop control system are analyzed based on Lyapunov theory. Compared with traditional spacecraft attitude control methods, the proposed approach not only achieves the optimality of predefined performance metrics but also exhibits the potential to overcome vibration parameter drift through real-time data learning via the PI-RNN. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed method.