This article proposes a distributed containment-based critical bus voltage coregulation strategy of submicrogrids (SMGs) with positive minimum interevent times (MIETs) in a multimicrogrid system (MMGS). First, the feedback linearization technique allows us to deal with nonlinear distributed generator (DG) dynamics. The critical bus voltage regulation problem of an ac microgrid (MG) is transformed into an output feedback tracking problem of a linear multiagent system (MAS) containing nonlinear dynamics. In addition, an event-triggered strategy based on containment control is proposed. The strategy limits each critical bus voltage within a reasonable range while having a voltage difference between SMGs to allow power flow. Furthermore, an innovative trigger mechanism has been designed based on multiple measurement errors. Based on this mechanism, the controllers are updated in an acyclic manner at the moment of event sampling, saving computational resources and transmission load. In addition, the proposed event-triggering mechanism guarantees the absence of Zeno behavior and a strictly positive MIET between each DG event. It is also more practical than the traditional event triggering because the hardware constraint always imposes a positive minimum time constraint between two consecutive event times. The protocol proposed in this article is fully distributed and scalable and does not depend on global information about the network graph. Finally, simulation results verify the effectiveness of the strategy.