Extreme multi-label classification task deals with nowadays problems involving up to millions of labels. The extremely large number of labels requires efficient methods not only in terms of prediction performances but also in terms of time processing and memory management. Most recent works focus on representation learning approaches: embeddings allow to infer a semantic structured space with interesting generalization properties; the label prediction is often performed by using approximated nearest neighbors search. Recent works in Language Modeling and especially in Question Answering have shown increasing performances using the hyperbolic space to learn the representation. The Poincaré ball model is indeed more relevant to represent ontology than the euclidean space. In this work, we propose to explore representation learning in hyperbolic space in the context of extreme classification. The proposed model performs a joint embedding of examples and labels. Most of the embedding methods for extreme classification only learn example embedding. Thus in order to structure the space, they require to precompute examples neighborhood. In our approach, learning a joint embedding allows structuring the space without any expensive preprocessing. Experiments conducted on real-world datasets show the performances of our model compared to state of the art.