The conventional distributed secondary control of islanded microgrids (MGs) often requires each distributed generator (DG) to communicate with its neighboring DGs successively with a small fixed sampling period, which is neither economical nor efficient for MGs due to its redundant communications. To this end, this paper proposes a distributed event-triggered control strategy for the secondary control in MGs to reduce the requirement for communications. By designing the trigger function and the trigger condition for each DG with Lyapunov method, the secondary control aim is achieved with an exponential convergence rate only when each DG communicating with its neighbors at some particular events. In addition, a proper trigger condition checking period is provided based on the proposed event-triggered control scheme, with which the computation requirement can be reduced. The proposed distribute event-triggered secondary control scheme has been tested on a cyber-physical MG, and its effectiveness is validated by the simulation results.