There are several opportunities for automation in healthcare that can improve clinician throughput. One such example is assistive tools to document diagnosis codes when clinicians write notes. We study the automation of medical code prediction using curriculum learning, which is a training strategy for machine learning models that gradually increases the hardness of the learning tasks from easy to difficult. One of the challenges in curriculum learning is the design of curricula -- i.e., in the sequential design of tasks that gradually increase in difficulty. We propose Hierarchical Curriculum Learning (HiCu), an algorithm that uses graph structure in the space of outputs to design curricula for multi-label classification. We create curricula for multi-label classification models that predict ICD diagnosis and procedure codes from natural language descriptions of patients. By leveraging the hierarchy of ICD codes, which groups diagnosis codes based on various organ systems in the human body, we find that our proposed curricula improve the generalization of neural network-based predictive models across recurrent, convolutional, and transformer-based architectures. Our code is available at https://github.com/wren93/HiCu-ICD.