DC microgrids ease the integration of renewables and can be easily put together with plug-and-play operation. However, most control techniques in DC microgrids focus on voltage regulation without considering its economical operation. Furthermore, the economic dispatch of different generation is usually implemented at a higher control level for long-term operation, and this is subject to prediction uncertainties. Therefore, this paper proposes a novel distributed model predictive control strategy for economic dispatch of the system generation and voltage restoration at the same time-scale in DC microgrids. Each distributed generator achieves both objectives using local measurements and predicted information from neighboring units. Experimental results in a 6 kW testbed validate the distributed structure of the predictive controller for communication problems and in the presence of plug-and-play scenarios without modifying and/or adjusting the control system parameters.