The recent advances in mobile technologies have resulted in Internet of Things (IoT)-enabled devices becoming more pervasive and integrated into our daily lives. The security challenges that need to be overcome mainly stem from the open nature of a wireless medium, such as a Wi-Fi network. An impersonation attack is an attack in which an adversary is disguised as a legitimate party in a system or communications protocol. The connected devices are pervasive, generating high-dimensional data on a large scale, which complicates simultaneous detections. Feature learning, however, can circumvent the potential problems that could be caused by the large-volume nature of network data. This paper thus proposes a novel deep-feature extraction and selection (D-FES), which combines stacked feature extraction and weighted feature selection. The stacked autoencoding is capable of providing representations that are more meaningful by reconstructing the relevant information from its raw inputs. We then combine this with modified weighted feature selection inspired by an existing shallow-structured machine learner. We finally demonstrate the ability of the condensed set of features to reduce the bias of a machine learner model as well as the computational complexity. Our experimental results on a well-referenced Wi-Fi network benchmark data set, namely, the Aegean Wi-Fi Intrusion data set, prove the usefulness and the utility of the proposed D-FES by achieving a detection accuracy of 99.918% and a false alarm rate of 0.012%, which is the most accurate detection of impersonation attacks reported in the literature.