To address the difficulty of simultaneously achieving voltage restoration, current sharing, and economic operation in distributed secondary control of DC microgrids, as well as the limitation of slow convergence in existing approaches, a prescribed-time game-based distributed secondary control strategy is proposed. By constructing a multi-objective cost function that incorporates voltage restoration error, current sharing error, and generation cost, the coordinated regulation problem among distributed generators is formulated as a non-cooperative game. Based on a prescribed-time coordinated control framework, a distributed game-based decision-making algorithm is developed such that the decision variables of each distributed generator converge to the Nash equilibrium within a specified time, where the convergence time is independent of both the initial states and control parameters. Furthermore, a discrete communication mechanism is introduced to effectively reduce the communication burden caused by continuous information exchange, thereby enhancing the implementability under communication resource constraints. Finally, simulations are conducted on a Matlab/Simulink platform under multiple scenarios, including load switching, plug-and-play operation, and weight variation. The results demonstrate that the proposed method can achieve bus voltage restoration and proportional current sharing within the prescribed time while attaining a favorable trade-off between regulation performance and economic operation.