This paper presents a distributed data-driven control to regulate the voltage in an alternate current microgrid (MG). Following the hierarchical control frame for MGs, a secondary control for voltage is designed with a data-driven strategy using the Koopman operator. The Koopman operator approach represents the nonlinear behavior of voltage as a linear problem in the space of observables or lifted space. The representation in the lifted space is used together with linear consensus to design a model predictive control (MPC). The complete algorithm is proved in an MG model that includes changes in load, transmission lines, and the communication graph. The data-driven model regulates the voltage using a distributed approach based only on local measurements, and includes reactive power constraints and control cost minimization.