We propose unsupervised embedding adaptation for the downstream few-shot classification task. Based on findings that deep neural networks learn to generalize before memorizing, we develop Early-Stage Feature Reconstruction (ESFR) --- a novel adaptation scheme with feature reconstruction and dimensionality-driven early stopping that finds generalizable features. Incorporating ESFR consistently improves the performance of baseline methods on all standard settings, including the recently proposed transductive method. ESFR used in conjunction with the transductive method further achieves state-of-the-art performance on mini-ImageNet, tiered-ImageNet, and CUB; especially with 1.2%~2.0% improvements in accuracy over the previous best performing method on 1-shot setting.