Existing few-shot learning (FSL) methods make the implicit assumption that the few target class samples are from the same domain as the source class samples. However, in practice this assumption is often invalid -- the target classes could come from a different domain. This poses an additional challenge of domain adaptation (DA) with few training samples. In this paper, the problem of domain-adaptive few-shot learning (DA-FSL) is tackled, which requires solving FSL and DA in a unified framework. To this end, we propose a novel domain-adversarial prototypical network (DAPN) model. It is designed to address a specific challenge in DA-FSL: the DA objective means that the source and target data distributions need to be aligned, typically through a shared domain-adaptive feature embedding space; but the FSL objective dictates that the target domain per class distribution must be different from that of any source domain class, meaning aligning the distributions across domains may harm the FSL performance. How to achieve global domain distribution alignment whilst maintaining source/target per-class discriminativeness thus becomes the key. Our solution is to explicitly enhance the source/target per-class separation before domain-adaptive feature embedding learning in the DAPN, in order to alleviate the negative effect of domain alignment on FSL. Extensive experiments show that our DAPN outperforms the state-of-the-art FSL and DA models, as well as their na\"ive combinations. The code is available at https://github.com/dingmyu/DAPN.