In this paper, a novel adaptive tracking control technique is developed for multiple-input-multiple-output (MIMO) nonlinear systems with model uncertainty and under output constraints occurring in a limited time interval (OCOLT). The OCOLT, which is a type of constraints occurring some time after (rather than from the beginning of) system operation and with limited duration, can be found in many practical systems and has not been effectively addressed in the literature up to now. By designing a new shift function and with the aid of barrier functions, the constrained system is transformed into an unconstrained one. A new disturbance observer then is designed to estimate unknown disturbances. The resultant control method is able to not only address the OCOLT, but also deal with the constraint-free output case and the infinite-time constrained one (i.e., constraints existing for all $t\geq 0$) without the need to revise the control structure. Finally, The effectiveness of the proposed technique is assessed in simulation.