Carbon capture and storage technology is a means to permanently store carbon dioxide (CO2) in suitable geologic formations, such as depleted oil and gas reservoirs and saline aquifers. The potential of depleted carbonates reservoirs for being a secure storage site has been assessed in several studies based on the key storage aspects. However, minor attention has been given to rock type and the potential compaction of carbonates at different injection rates when geochemical interactions posed by supercritical CO2 reduces their elastic properties and strength. In this study, limestone samples were tested to investigate changes in their physical and mechanical characteristics once flooded by CO2 at a very low injection rate. The results obtained indicate that an excessive pressure drop might be experienced even under a very low injection rate because of continuous dissolution of carbonates in the presence of CO2 and brine. Creation of wormholes and the dissolution of the matrix were also observed through scanning electron microscope, computerized tomography scan, and nuclear magnetic resonance tests. It was also observed that the elastic parameters and the strength of the limestone samples may significantly decrease after CO2 flooding, which might be linked to calcite dissolution and weakening of the solid skeleton.