Tabular data is prevalent across various machine learning domains. Yet, the inherent heterogeneities in attribute and class spaces across different tabular datasets hinder the effective sharing of knowledge, limiting a tabular model to benefit from other datasets. In this paper, we propose Tabular data Pre-Training via Meta-representation (TabPTM), which allows one tabular model pre-training on a set of heterogeneous datasets. Then, this pre-trained model can be directly applied to unseen datasets that have diverse attributes and classes without additional training. Specifically, TabPTM represents an instance through its distance to a fixed number of prototypes, thereby standardizing heterogeneous tabular datasets. A deep neural network is then trained to associate these meta-representations with dataset-specific classification confidences, endowing TabPTM with the ability of training-free generalization. Experiments validate that TabPTM achieves promising performance in new datasets, even under few-shot scenarios.