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Multimodal sentiment analysis, which learns a model to process multiple modalities simultaneously and predict a sentiment value, is an important area of affective computing. Modeling sequential intra-modal information and enhancing cross-modal interactions are crucial to multimodal sentiment analysis. In this paper, we propose MSAmba, a novel hybrid Mamba-based architecture for multimodal sentiment analysis, consisting of two core blocks: Intra-Modal Sequential Mamba (ISM) block and Cross-Modal Hybrid Mamba (CHM) block, to comprehensively address the above-mentioned challenges with hybrid state space models. Firstly, the ISM block models the sequential information within each modality in a bi-directional manner with the assistance of global information. Subsequently, the CHM blocks explicitly model centralized cross-modal interaction with a hybrid combination of Mamba and attention mechanism to facilitate information fusion across modalities. Finally, joint learning of the intra-modal tokens and cross-modal tokens is utilized to predict the sentiment values. This paper serves as one of the pioneering works to unravel the outstanding performances and great research potential of Mamba-based methods in the task of multimodal sentiment analysis. Experiments on CMU-MOSI, CMU-MOSEI and CH-SIMS demonstrate the superior performance of the proposed MSAmba over prior Transformer-based and CNN-based methods.