Presented are mobile charging stations for recharging electrified vehicles, methods for making/using such mobile charging stations, and parking facilities equipped with such mobile charging stations. A mobile charging station includes a frame with drive wheels and a prime mover operable to drive the wheels to propel the charging station. A hydrogen storage container and fuel cell are mounted to the frame. The fuel cell oxidizes hydrogen received from the storage container to generate electrical current. An electrical coupling mechanism connects the fuel cell to a battery pack of an electric-drive vehicle. A resident or remote controller is programmed to receive charge requests to recharge vehicles, and responsively determines path plan data for the mobile charging station. The controller commands the prime mover to propel the mobile charging station from the charger's origin to a charger destination, and enables the fuel cell to transmit electrical current to the vehicle.