Zero-shot learning (ZSL) aims to recognize unseen classes by transferring semantic knowledge from seen classes to unseen ones, guided by semantic information. To this end, existing works have demonstrated remarkable performance by utilizing global visual features from Convolutional Neural Networks (CNNs) or Vision Transformers (ViTs) for visual-semantic interactions. Due to the limited receptive fields of CNNs and the quadratic complexity of ViTs, however, these visual backbones achieve suboptimal visual-semantic interactions. In this paper, motivated by the visual state space model (i.e., Vision Mamba), which is capable of capturing long-range dependencies and modeling complex visual dynamics, we propose a parameter-efficient ZSL framework called \textbf{ZeroMamba} to advance ZSL. Our ZeroMamba comprises three key components: Semantic-aware Local Projection (SLP), Global Representation Learning (GRL), and Semantic Fusion (SeF). Specifically, SLP integrates semantic embeddings to map visual features to local semantic-related representations, while GRL encourages the model to learn global semantic representations. SeF combines these two semantic representations to enhance the discriminability of semantic features. We incorporate these designs into Vision Mamba, forming an end-to-end ZSL framework. As a result, the learned semantic representations are better suited for classification. Through extensive experiments on four prominent ZSL benchmarks, ZeroMamba demonstrates superior performance, significantly outperforming the state-of-the-art (i.e., CNN-based and ViT-based) methods under both conventional ZSL (CZSL) and generalized ZSL (GZSL) settings. Code is available at: https://anonymous.4open.science/r/ZeroMamba.