During the outbreak of the novel coronavirus pneumonia (COVID-19), there is a huge demand for medical masks. A mask manufacturer often receives a large amount of orders that are beyond its capability. Therefore, it is of critical importance for the manufacturer to schedule mask production tasks as efficiently as possible. However, existing scheduling methods typically require a considerable amount of computational resources and, therefore, cannot effectively cope with the surge of orders. In this paper, we propose an end-to-end neural network for scheduling real-time production tasks. The neural network takes a sequence of production tasks as inputs to predict a distribution over different schedules, employs reinforcement learning to optimize network parameters using the negative total tardiness as the reward signal, and finally produces a high-quality solution to the scheduling problem. We applied the proposed approach to schedule emergency production tasks for a medical mask manufacturer during the peak of COVID-19 in China. Computational results show that the neural network scheduler can solve problem instances with hundreds of tasks within seconds. The objective function value (i.e., the total weighted tardiness) produced by the neural network scheduler is significantly better than those of existing constructive heuristics, and is very close to those of the state-of-the-art metaheuristics whose computational time is unaffordable in practice.