The present study aimed to develop a numerical simulation to predict the chemistry change of groundwater heavy metals pollution (mainly arsenic pollution) in the Southern region of the Punjab Province of Pakistan. This work is the first attempt in modelling the transport of groundwater heavy metals pollution in the area using a 1D reactive transport model. PHREEQC was employed to perform the numerical simulation. The conceptual model represented the 1D numerical transport model with the homogenous mineral composition having uniform transport of the municipal wastewater. A 100 m column—20 cell transport model was used with a time step of 5000 years, making a simulated timescale of 100,000 years. The simulation was carried out using quartz, illite, and calcite kinetics. Arsenic sorption kinetics were also incorporated in the simulation. The results revealed that the concentrations of four out of ten heavy metals and three out of eight inorganic ions were above the drinking water quality standards at the end of the simulation making the groundwater unsafe for drinking purposes. The arsenic concentration was found out to be 3.79 mg/l against 100,000 year which is 379 times the international drinking water standard and about 76 times the national drinking water standard for arsenic. It is concluded that the groundwater, regardless of the natural soil treatment, will be highly contaminated after 100,000 years, particularly with heavy metals including arsenic, cadmium, iron, lead, and nickel. The groundwater quality can be enhanced by appreciating the preventive measures recommended in this study.