Calcium dissolution is a crucial process during the supercritical carbonation of cement-based materials, significantly influencing the carbonation process due to its impact on pore structure and chemical kinetics. Therefore, considering calcium dissolution is essential for accurately characterizing and predicting the carbonation behavior. However, current theories and models of supercritical carbonation generally overlook this factor. This paper presents a multiphysics theory that integrates calcium dissolution into the supercritical carbonation model for cement-based materials. In this model, macroscopic phenomena, including mass transport, kinetic energy transfer, heat transfer, and chemical reactions, are coupled with microscopic processes of calcium dissolution, transport, and ionic reactions. The multiphysics model is derived by combining the partial differential equations governing these physical and chemical processes. It serves as the theoretical foundation for the numerical model, which is detailed in Part II. This study provides a comprehensive understanding of the coupling mechanisms between carbonation and calcium dissolution.