Artificial Intelligence (AI)-aided drug discovery is an active research field, yet AI models often exhibit poor accuracy in regression tasks for molecular property prediction, and perform catastrophically poorly for out-of-distribution (OOD) molecules. Here, we present MolRuleLoss, a substructure-substitution-rule-informed framework that improves the accuracy and generalizability of multiple molecular property regression models (MPRMs) such as GEM and UniMol for diverse molecular property prediction tasks. MolRuleLoss incorporates partial derivative constraints for substructure substitution rules (SSRs) into an MPRM's loss function. When using GEM models for predicting lipophilicity, water solubility, and solvation-free energy (using lipophilicity, ESOL, and freeSolv datasets from MoleculeNet), the root mean squared error (RMSE) values with and without MolRuleLoss were 0.587 vs. 0.660, 0.777 vs. 0.798, and 1.252 vs. 1.877, respectively, representing 2.6-33.3% performance improvements. We show that both the number and the quality of SSRs contribute to the magnitude of prediction accuracy gains obtained upon adding MolRuleLoss to an MPRM. MolRuleLoss improved the generalizability of MPRMs for "activity cliff" molecules in a lipophilicity prediction task and improved the generalizability of MPRMs for OOD molecules in a melting point prediction task. In a molecular weight prediction task for OOD molecules, MolRuleLoss reduced the RMSE value of a GEM model from 29.507 to 0.007. We also provide a formal demonstration that the upper bound of the variation for property change of SSRs is positively correlated with an MPRM's error. Together, we show that using the MolRuleLoss framework as a bolt-on boosts the prediction accuracy and generalizability of multiple MPRMs, supporting diverse applications in areas like cheminformatics and AI-aided drug discovery.