Traffic image restoration under adverse weather conditions remains a critical challenge for intelligent transportation systems. Existing methods primarily focus on spatial-domain modeling but neglect frequency-domain priors. Although the emerging Mamba architecture excels at long-range dependency modeling through patch-wise correlation analysis, its potential for frequency-domain feature extraction remains unexplored. To address this, we propose Frequency-Aware Mamba (FAMamba), a novel framework that integrates frequency guidance with sequence modeling for efficient image restoration. Our architecture consists of two key components: (1) a Dual-Branch Feature Extraction Block (DFEB) that enhances local-global interaction via bidirectional 2D frequency-adaptive scanning, dynamically adjusting traversal paths based on sub-band texture distributions; and (2) a Prior-Guided Block (PGB) that refines texture details through wavelet-based high-frequency residual learning, enabling high-quality image reconstruction with precise details. Meanwhile, we design a novel Adaptive Frequency Scanning Mechanism (AFSM) for the Mamba architecture, which enables the Mamba to achieve frequency-domain scanning across distinct subgraphs, thereby fully leveraging the texture distribution characteristics inherent in subgraph structures. Extensive experiments demonstrate the efficiency and effectiveness of FAMamba.