Fine-grained emotion classification (FEC) is a challenging task. Specifically, FEC needs to handle subtle nuance between labels, which can be complex and confusing. Most existing models only address text classification problem in the euclidean space, which we believe may not be the optimal solution as labels of close semantic (e.g., afraid and terrified) may not be differentiated in such space, which harms the performance. In this paper, we propose HypEmo, a novel framework that can integrate hyperbolic embeddings to improve the FEC task. First, we learn label embeddings in the hyperbolic space to better capture their hierarchical structure, and then our model projects contextualized representations to the hyperbolic space to compute the distance between samples and labels. Experimental results show that incorporating such distance to weight cross entropy loss substantially improve the performance on two benchmark datasets, with around 3\% improvement compared to previous state-of-the-art, and could even improve up to 8.6\% when the labels are hard to distinguish. Code is available at https://github.com/dinobby/HypEmo.