This paper proposes a learning control framework for the robotic manipulator’s dynamic tracking task demanding fixed-time convergence and constrained output. In contrast with model-dependent methods, the proposed solution deals with unknown manipulator dynamics and external disturbances by virtue of a recurrent neural network (RNN)-based online approximator. First, a time-varying tangent-type barrier Lyapunov function (BLF) is introduced to construct a fixed-time virtual controller. Then, the RNN approximator is embedded in the closed-loop system to compensate for the lumped unknown term in the feedforward loop. Finally, we devise a novel fixed-time, output-constrained neural learning controller by integrating the BLF and RNN approximator into the main framework of the dynamic surface control (DSC). The proposed scheme not only guarantees the tracking errors converge to the small neighborhoods about the origin in a fixed time, but also preserves the actual trajectories always within the prescribed ranges and thus improves the tracking accuracy. Experiment results illustrate the excellent tracking performance and verify the effectiveness of the online RNN estimate for unknown dynamics and external disturbances.