This paper presents a Distributed Model Predictive Control (DMPC)-based algorithm for distributed and coordinated voltage control of wind power plants. Under the proposed approach, voltage magnitude at the point of connection of wind power plants is optimally controlled to meet voltage requirements. In a conventional centralized approach, each wind power farm tracks the control signals set by the Transmission System Operator but DMPC responds locally to mitigate the voltage deviations without the central commands. The problem is cast as one of optimal control, which is solved at every time step by a distributed optimization. A dual decomposition scheme is proposed to solve the distributed optimization problem where the voltages magnitude of the common nodes are used as a consensus term for the coordination. In order to extend the applicability of this control, the proposed DMPC is carefully designed in such a way that it does not require any change in the inner control of the electrical machines, controls or compensators. The algorithm has been tested on an IEEE 9-bus system with two wind power plants and on an IEEE 14-bus system with three power plants. In both cases, the plants are not directly connected. Following an analysis of the achievable performance and the computational resources consumed by the local algorithm, the results of the simulations confirm that the proposed control approach is suitable for the voltage coordination of wind power plants with acceptable scalable results.