Stereo disparity estimation is crucial for obtaining depth information in robot-assisted minimally invasive surgery (RAMIS). While current deep learning methods have made significant advancements, challenges remain in achieving an optimal balance between accuracy, robustness, and inference speed. To address these challenges, we propose the StereoMamba architecture, which is specifically designed for stereo disparity estimation in RAMIS. Our approach is based on a novel Feature Extraction Mamba (FE-Mamba) module, which enhances long-range spatial dependencies both within and across stereo images. To effectively integrate multi-scale features from FE-Mamba, we then introduce a novel Multidimensional Feature Fusion (MFF) module. Experiments against the state-of-the-art on the ex-vivo SCARED benchmark demonstrate that StereoMamba achieves superior performance on EPE of 2.64 px and depth MAE of 2.55 mm, the second-best performance on Bad2 of 41.49% and Bad3 of 26.99%, while maintaining an inference speed of 21.28 FPS for a pair of high-resolution images (1280*1024), striking the optimum balance between accuracy, robustness, and efficiency. Furthermore, by comparing synthesized right images, generated from warping left images using the generated disparity maps, with the actual right image, StereoMamba achieves the best average SSIM (0.8970) and PSNR (16.0761), exhibiting strong zero-shot generalization on the in-vivo RIS2017 and StereoMIS datasets.