Interpolative data augmentation has proven to be effective for NLP tasks. Despite its merits, the sample selection process in mixup is random, which might make it difficult for the model to generalize better and converge faster. We propose CIAug, a novel curriculum-based learning method that builds upon mixup. It leverages the relative position of samples in hyperbolic embedding space as a complexity measure to gradually mix up increasingly difficult and diverse samples along training. CIAug achieves state-of-the-art results over existing interpolative augmentation methods on 10 benchmark datasets across 4 languages in text classification and named-entity recognition tasks. It also converges and achieves benchmark F1 scores 3 times faster. We empirically analyze the various components of CIAug, and evaluate its robustness against adversarial attacks.