Smart waterflooding is one of the most practical emerging methods of enhanced oil recovery in carbonate reservoirs. In this study, the effect of salt type and its concentration in smart water on oil recovery from a carbonate reservoir rock is investigated. A series of experimental measurements, including zeta potential (ZP), interfacial tension (IFT), and contact angle (CA), were conducted to examine the effect of ions on the oil/brine/rock interaction. IFT, ZP, and CA were also used as screening methods to select effective solutions for flooding experiments. The results of the study show that synthesized brines containing sodium acetate and potassium acetate salts have a significant effect on the reduction of IFT; however, rock surface wettability due to such brines is insignificant. The presence of organic salts in the injected water can alter the properties of the fluid and rock surface, leading to improved oil recovery. The salts can reduce the interfacial tension between the oil and water phases, making it easier for the water to displace and mobilize trapped oil. This effect is particularly beneficial in reservoirs with high oil–water interfacial tension as it enhances the capillary forces and improves the sweep efficiency. Smart water with sodium acetate (MSW.NaOAc) caused a 7% increase in oil production in the tertiary injection process due to IFT and CA reduction. The secondary injection of MSW.NaOAc led to an oil production efficiency of 76%, which is 10% higher than that of the secondary injection of seawater (SW), confirming the effectiveness of acetate ions in enhancing oil recovery. Doubling the concentration of sulfate ions in modified SW (MSW.NaOAc.2S) caused a 19% increase in oil production in tertiary injections after SW flooding. The secondary injection of MSW.NaOAc.2S produced a 13% increase in the recovery factor compared to SW flooding in the secondary mode. The main driving mechanism for oil mobilization was found to be wettability alteration, which is supported by the analyses of CA and ZP. This study confirms that the salt type and concentration present in a brine solution play a vital role in the movement of trapped oil in carbonate reservoirs.