Real-world classification tasks are frequently required to work in an open-set setting. This is especially challenging for few-shot learning problems due to the small sample size for each known category, which prevents existing open-set methods from working effectively; however, most multiclass few-shot methods are limited to closed-set scenarios. In this work, we address the problem of few-shot open-set classification by first proposing methods for few-shot one-class classification and then extending them to few-shot multiclass open-set classification. We introduce two independent few-shot one-class classification methods: Meta Binary Cross-Entropy (Meta-BCE), which learns a separate feature representation for one-class classification, and One-Class Meta-Learning (OCML), which learns to generate one-class classifiers given standard multiclass feature representation. Both methods can augment any existing few-shot learning method without requiring retraining to work in a few-shot multiclass open-set setting without degrading its closed-set performance. We demonstrate the benefits and drawbacks of both methods in different problem settings and evaluate them on three standard benchmark datasets, miniImageNet, tieredImageNet, and Caltech-UCSD-Birds-200-2011, where they surpass the state-of-the-art methods in the few-shot multiclass open-set and few-shot one-class tasks.