In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual data and users' purchase history. During training, we apply a multi-task learning framework that considers both hyperbolic and Euclidean distances in the loss function. Our experiments on three data sets show that our model performs better than previous models trained in Euclidean space only, confirming the effectiveness of our model. Our ablation studies show that multi-task learning plays a key role, and removing the Euclidean loss substantially deteriorates the model performance.