Extreme classification and Neural Architecture Search (NAS) are research topics which have recently gained a lot of interest. While the former has been mainly 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 task of extreme multilabel classification (XMC). We propose a neuro-evolution approach, which was found to be the most suitable for a variety of tasks. Our NAS method automatically finds architectures that give competitive results with respect to the state of the art (and superior to other methods) with faster convergence. In addition, we perform analysis of the weights of the architecture blocks to provide insight into the importance of different operations that have been selected by the method.