During the chemical interactions between fluid and minerals in different geological processes, it is of high importance to predict where secondary precipitates form in the porous rocks as it helps correctly predict the hydrodynamic properties of the porous media. The reactive transport models developed for this purpose need to account for the nucleation process which is probabilistic by nature. To our knowledge, the probabilistic nature of nucleation based on the classical nucleation theory has not been accounted for previously in reactive transport models. In this study, we develop a new probabilistic nucleation model and incorporate it into a pore-scale reactive transport solver to simulate the mineral nucleation and growth in the porous media. Simulations are performed for different supersaturations, growth rates, and flow rates using a single-component mineral reaction. Simulations show that initial supersaturations strongly affect the pattern of secondary precipitate formation. Higher initial supersaturations lead to more uniformly dispersed nucleation on all the grains, while the lower initial supersaturations result in more isolated patterns. Decreasing the growth rate favors the formation of uniformly dispersed nuclei, whereas higher growth rates cause more isolated nucleation. Injection of fluid with a higher velocity gives rise to more precipitation. Moreover, comparison of probabilistic and deterministic nucleation showed that the isolated nucleation patterns cannot be modeled using the deterministic approach. The results showed that permeability for the porous media is influenced by the pattern of secondary precipitate growth and it is demonstrated that generally, the permeability has a direct relation with the initial supersaturation and an inverse relation with the growth rate and the flow rate. Finally, the model was applied for simulation of calcite nucleation and growth on quartz grains. The calcite nucleation and growth exhibit similar behavior to those observed for single-species simulations.