In many fields, such as functional genomics or finance, data analysis, and predictive modeling are always challenging for the course of dimensionality and noisy data. In these cases, effective feature selection algorithms, based on Machine and Deep Learning, can perform and improve the identification of important features, leading to more treatable problems in terms of dimensionality. The paper proposes a novel algorithm to perform Feature Selection on highly dimensional data, which exploits the reconstruction capabilities of autoencoders and an ad-hoc defined Explainable Artificial Intelligence-based score to select the most informative feature for predictions. We benchmark such an approach on several state-of-the-art datasets and against the previously proposed algorithm in the literature, showcasing its effectiveness.