In this study, the response surface method is used to develop a model for analyzing and optimizing zinc leaching experiments. An investigation into the leaching kinetics of smithsonite in ammonium citrate solution is also conducted. A model of kinetics is studied in order to represent these effects. The experimental data show that an increase in the solution temperature, concentration, and stirring speed has a positive impact on the leaching rate, while an increase in the particle size has a negative impact on it. The optimal experimental conditions consist of a leaching temperature of 70 °C, ammonium citrate concentration of 5 mol/L, particle size of 38 µm, and rotational speed of 1000 rpm. Under these optimal conditions, the leaching rate of zinc from smithsonite is 83.51%. It is speculated that the kinetic model will change when the temperature is higher than 60 °C. When the temperature is lower than 60 °C, the leaching process is under the control of the shrinking core model of the surface chemical reactions. The calculated activation energy of the leaching reaction is equal to 42 kJ/mol. The model of the leaching process can be described by the following equation: 1−1−x1/3=k0⋅(C)0.6181⋅r0−0.5868⋅SS0.6901exp−42/RT]t. This demonstrates that an ammonium citrate solution can be used in the leaching process of zinc in smithsonite as an effective and clean leaching agent.