This work presents a novel approach to tabular data prediction leveraging graph structure learning and graph neural networks. Despite the prevalence of tabular data in real-world applications, traditional deep learning methods often overlook the potentially valuable associations between data instances. Such associations can offer beneficial insights for classification tasks, as instances may exhibit similar patterns of correlations among features and target labels. This information can be exploited by graph neural networks, necessitating robust graph structures. However, existing studies primarily focus on improving graph structure from noisy data, largely neglecting the possibility of deriving graph structures from tabular data. We present a novel solution, Tabular Graph Structure Learning (TabGSL), to enhance tabular data prediction by simultaneously learning instance correlation and feature interaction within a unified framework. This is achieved through a proposed graph contrastive learning module, along with transformer-based feature extractor and graph neural network. Comprehensive experiments conducted on 30 benchmark tabular datasets demonstrate that TabGSL markedly outperforms both tree-based models and recent deep learning-based tabular models. Visualizations of the learned instance embeddings further substantiate the effectiveness of TabGSL.