Free-floating space robots have emerged as critical unmanned platforms for long-term in-orbit services due to their high mobility and extended operational lifespan. However, external disturbances caused by dynamic space environments, as well as model uncertainties arising from fuel consumption and inaccurate system parameter identification, significantly increase the challenges of high-precision control for space robotic systems. This paper proposes a disturbance compensation-based model predictive tracking control method for free-floating space robots subject to joint disturbance torques and model uncertainties. A fixed-time disturbance observer is designed based on fixed-time stability theory, ensuring that the disturbance estimation error converges within a fixed upper bound independent of initial errors. The estimated disturbances are then compensated into the model predictive controller to enhance prediction model accuracy under lumped disturbance conditions. Furthermore, by leveraging the receding horizon optimization characteristics of model predictive control, high-precision trajectory tracking is achieved while satisfying system constraints. The stability of the proposed disturbance observer and the compensation-based model predictive controller is rigorously proven. Numerical simulations are conducted to validate the effectiveness of the proposed approach in improving control precision and disturbance rejection capabilities.