Speech restoration aims at restoring high quality speech in the presence of a diverse set of distortions. Although several deep learning paradigms have been studied for this task, the power of the recently emerging language models has not been fully explored. In this paper, we propose MaskSR, a masked language model capable of restoring full-band 44.1 kHz speech jointly considering noise, reverb, clipping, and low bandwidth. MaskSR works with discrete acoustic tokens extracted using a pre-trained neural codec. During training, MaskSR is optimized to predict randomly masked tokens extracted from the high quality target speech, conditioned on the corrupted speech with various distortions. During inference, MaskSR reconstructs the target speech tokens with efficient iterative sampling. Extensive experiments show that MaskSR obtains competitive results on both the full-band speech restoration task and also on sub-tasks compared with a wide range of models.