It is nontrivial to achieve adaptive asymptotic tracking control of multi-input multi-output (MIMO) nonlinear systems subject to asymmetric yet time-varying output constraint and nonparametric uncertainties. The problem will become even challenging when the event-triggered mechanism via controller-to-actuator channel is considered as it may impose additional design difficulty caused by the high-order gain matrix. In this article, we present a new event-based control solution by using the following steps. First, by constructing a new output-dependent mapping function, not only the limit on constraining boundaries is not required but also the cases with and without constraint can be handled directly and uniformly without changing the control structure; Second, due to the introduction of event-triggered rule, it is difficult (even impossible) to guarantee the positive definite property of the “virtual” high-order gain matrix; Hence by imposing a reasonable condition on the original high-order gain matrix, such difficulty in the event-triggered control design is solved and the widely used assumption in most existing results of MIMO systems is removed; Furthermore, unlike the corresponding uniformly bounded tracking results, by employing an integrable function coping with nonparametric uncertainties, asymptotic tracking can be achieved. A simulation example is given to illustrate the effectiveness of the developed theoretical result.