Training deep learning models for semantic occupancy prediction is challenging due to factors such as a large number of occupancy cells, severe occlusion, limited visual cues, complicated driving scenarios, etc. Recent methods often adopt transformer-based architectures given their strong capability in learning input-conditioned weights and long-range relationships. However, transformer-based networks are notorious for their quadratic computation complexity, seriously undermining their efficacy and deployment in semantic occupancy prediction. Inspired by the global modeling and linear computation complexity of the Mamba architecture, we present the first Mamba-based network for semantic occupancy prediction, termed OccMamba. However, directly applying the Mamba architecture to the occupancy prediction task yields unsatisfactory performance due to the inherent domain gap between the linguistic and 3D domains. To relieve this problem, we present a simple yet effective 3D-to-1D reordering operation, i.e., height-prioritized 2D Hilbert expansion. It can maximally retain the spatial structure of point clouds as well as facilitate the processing of Mamba blocks. Our OccMamba achieves state-of-the-art performance on three prevalent occupancy prediction benchmarks, including OpenOccupancy, SemanticKITTI and SemanticPOSS. Notably, on OpenOccupancy, our OccMamba outperforms the previous state-of-the-art Co-Occ by 3.1% IoU and 3.2% mIoU, respectively. Codes will be released upon publication.