Convolutional Neural Networks (CNNs) and Transformers are the most popular architectures for medical image segmentation. However, both have limitations in handling long-range dependencies due to their inherent locality and computational complexity, respectively. To address this challenge, we introduce FM-Mamba, a general-purpose network for CT image segmentation. Inspired by the State Space Sequence Models (SSMs), a new family of deep sequence models known for their strong capability in handling long sequences with fewer parameters, we design a hybrid FM-SSM block that integrates the local frequency domain feature extraction with the abilities of SSMs for capturing the long-range dependency. This module ensures that the model captures global features with fewer parameters while reducing the difficulty of the model in identifying segmentation boundaries. In addition, FM-Mamba employs an expansion technique for SSM's A-matrix, which enables it to guarantee excellent inference capabilities even when faced with large size images. We conducted experiments on the publicly available CT-ORG and Synapse multi-organ segmentation datasets. The results reveal that FM-Mamba outperforms state-of-the-art CNN-based and Transformer-based segmentation networks. This advancement opens new avenues for efficient long-range dependency modeling in medical image analysis.