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Medical imaging faces significant challenges in single-domain generalization (SDG) due to the diversity of imaging devices and the variability among data collection centers. To address these challenges, we propose \textbf{TinyMIG}, a framework designed to transfer generalization capabilities from vision foundation models to medical imaging SDG. TinyMIG aims to enable lightweight specialized models to mimic the strong generalization capabilities of foundation models in terms of both global feature distribution and local fine-grained details during training. Specifically, for global feature distribution, we propose a Global Distribution Consistency Learning strategy that mimics the prior distributions of the foundation model layer by layer. For local fine-grained details, we further design a Localized Representation Alignment method, which promotes semantic alignment and generalization distillation between the specialized model and the foundation model. These mechanisms collectively enable the specialized model to achieve robust performance in diverse medical imaging scenarios. Extensive experiments on large-scale benchmarks demonstrate that TinyMIG, with extremely low computational cost, significantly outperforms state-of-the-art models, showcasing its superior SDG capabilities. All the code and model weights will be publicly available.