Extreme multi-label classification (XMC) and Neural Architecture Search (NAS) are research topics, which have gain a lot of interest recently. While the former deals in supervised learning problems with extremely large number of labels in text and NLP domain, the latter has been mainly applied to much smaller tasks, mainly in image processing. In this study, we extend the scope of NAS to (XMC) tasks. We propose a neuro-evolution approach, that has been found most suitable for a variety of tasks. The proposed 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.