Feature selection has devoted a consistently great amount of effort to dimension reduction for various machine learning tasks. Existing feature selection models focus on selecting the most discriminative features for learning targets. However, this strategy is weak in handling two kinds of features, that is, the irrelevant and redundant ones, which are collectively referred to as noisy features. These features may hamper the construction of optimal low-dimensional subspaces and compromise the learning performance of downstream tasks. In this study, we propose a novel multi-label feature selection approach by embedding label correlations (dubbed ELC) to address these issues. Particularly, we extract label correlations for reliable label space structures and employ them to steer feature selection. In this way, label and feature spaces can be expected to be consistent and noisy features can be effectively eliminated. An extensive experimental evaluation on public benchmarks validated the superiority of ELC.