Tabular data synthesis is a key technique for protecting data privacy and addressing class imbalance, yet existing generative models struggle to capture the complex intrinsic structure of the data. To overcome this limitation, we propose TabGeoFlow, a novel geometric flow matching model for tabular data synthesis. The core innovation of TabGeoFlow is the injection of an explicit geometric inductive bias into the conditional flow matching framework. We decompose the learned vector field into local tangent and normal components of the data manifold. By dynamically suppressing the predicted normal component via a controlling loss function, we constrain the generative path to follow the data's intrinsic structure. Implemented with a shared backbone for parameter efficiency, TabGeoFlow outperforms existing baseline methods across multiple benchmark datasets, demonstrating superior data quality in terms of both statistical similarity and downstream machine learning utility.