We propose Curriculum by Masking (CBM), a novel state-of-the-art curriculum learning strategy that effectively creates an easy-to-hard training schedule via patch (token) masking, offering significant accuracy improvements over the conventional training regime and previous curriculum learning (CL) methods. CBM leverages gradient magnitudes to prioritize the masking of salient image regions via a novel masking algorithm and a novel masking block. Our approach enables controlling sample difficulty via the patch masking ratio, generating an effective easy-to-hard curriculum by gradually introducing harder samples as training progresses. CBM operates with two easily configurable parameters, i.e. the number of patches and the curriculum schedule, making it a versatile curriculum learning approach for object recognition and detection. We conduct experiments with various neural architectures, ranging from convolutional networks to vision transformers, on five benchmark data sets (CIFAR-10, CIFAR-100, ImageNet, Food-101 and PASCAL VOC), to compare CBM with conventional as well as curriculum-based training regimes. Our results reveal the superiority of our strategy compared with the state-of-the-art curriculum learning regimes. We also observe improvements in transfer learning contexts, where CBM surpasses previous work by considerable margins in terms of accuracy. We release our code for free non-commercial use at https://github.com/CroitoruAlin/CBM.