To investigate the coupled physical and chemical effects of injecting CO2-rich water into carbonate rock samples, we monitor the elastic and transport properties of six carbonate rocks, along with the calcium content and pH of the pore fluid under constant confining pressure. Carbonate samples range from calcite limestones containing dolomite to pure calcite mudstones, which allow us to study how mineral composition and microstructure affect the magnitude of the observed changes. The elastic properties of both the saturated and dry rock (i.e., rock frame) show a gradual loss of sstrength upon injection, as testified by the continuous decrease in the dry P- and S-wave velocity (and by proxy the bulk and shear moduli). The magnitude of the observed changes in the elastic properties varies among the samples, with a maximum relative change of 24.7% (871 m/s) and 21.2% (443 m/s) in P- and S- wave velocities, respectively. The decrease is also accompanied by a relative increase in permeability (up to 495%) and porosity (up to 19%). The observed changes likely derive from a change in microstructure, which is monitored over time via scanning electron microscopy. The variation in porosity results from two competing and interdependent processes: the chemical dissolution of calcite and the resulting mechanical compaction under pressure. The results of this study show that, upon injection of fluids that are in chemical disequilibrium with the hosting rock, the variation of the elastic properties cannot be described by existing rock-physics models.