In rehabilitation robot systems, communication and computational resources are often limited. Therefore, conserving either of these resources can significantly contribute to cost reduction, longer service life, and improved system reliability. Meanwhile, time-varying asymmetric constraints on the robot’s state are essential for ensuring its safe operation. In this paper, the problem of adaptive prescribed time tracking control for asymmetric time-varying constraints in rehabilitation robot systems over event-triggered communication is investigated. By introducing a parameter adaptive triggering mechanism with the help of a time-varying scale function, asymmetric time-varying constrained event-triggered control scheme is proposed, which has the following significant features compared with the existing results: (1) time-triggering is employed for both control updates and parameter adaptation, significantly conserving network resources; (2) when faced with asymmetric, time-varying constraints and unforeseen disturbances, the system’s tracking error reaches a predefined region within a specified timeframe; and (3) the full state of the system does not violate the asymmetric time-varying constraint intervals and eliminates the feasibility condition on the virtual controller. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation.