Few-shot text classification is a fundamental NLP task in which a model aims to classify text into a large number of categories, given only a few training examples per category. This paper explores data augmentation -- a technique particularly suitable for training with limited data -- for this few-shot, highly-multiclass text classification setting. On four diverse text classification tasks, we find that common data augmentation techniques can improve the performance of triplet networks by up to 3.0% on average. To further boost performance, we present a simple training strategy called curriculum data augmentation, which leverages curriculum learning by first training on only original examples and then introducing augmented data as training progresses. We explore a two-stage and a gradual schedule, and find that, compared with standard single-stage training, curriculum data augmentation trains faster, improves performance, and remains robust to high amounts of noising from augmentation.