Extreme classification and Neural Architecture Search (NAS) are research topics, which have gain a lot of interest recently. While the former has mainly been motivated and applied in e-commerce and Natural Language Processing (NLP) applications, the NAS approach has been applied to a small variety of tasks, mainly in image processing. In this study, we extend the scope of NAS to the extreme multi-label classification (XMC) tasks. We propose a neuro-evolution approach, that has been found most suitable for a variety of tasks. Our NAS method automatically finds architectures that give competitive results to the state of the art (and superior to other methods) with faster convergence. Furthermore, the weights of the architecture blocks have been analyzed to give insight on the importance of the various operations that have been selected by the method.