Abstract Groundwater models are essential tools for groundwater remediation and contamination risk assessment. However, due to the simplification or inaccurate representation of real‐world groundwater systems, model structural errors are widespread and unavoidable, leading to systematic biases in model predictions. Traditional Bayesian data‐driven methods (DDMs) aim to correct these model structural biases. Nonetheless, the error correction models developed by DDMs often lack physical mechanisms, resulting in predictions that violate fundamental physical principles, such as failing to satisfy mass conservation. This study proposes a general DDM coupled with physical constraints, explicitly incorporating physical constraints into the error correction model construction. By formulating a new likelihood function, this approach forces predictions to fit observations while satisfying physical constraints. The superiority of the DDM coupled with physical constraints was quantitatively evaluated in two case studies, a laboratory column fluoranthene transport simulation and a synthetic three‐dimensional groundwater contaminant transport simulation, with mass conservation as the physical constraint. The results reveal that the DDM without physical constraints produces predictions that significantly violate physical principles and exhibits moderate predictive performance. In contrast, the DDM with physical constraints effectively enhances prediction accuracy and substantially reduces mass balance errors. By imposing constraints on the identification process of parameters (physical parameters and hyperparameters), parameter overfitting was mitigated. Additionally, the implementation of mass conservation constraints effectively reduced prediction uncertainty. The proposed DDM coupled with physical constraints demonstrates robust adaptability to complex model structural errors and enhances the reliability of quantitative predictions of groundwater contamination under actual field conditions.