Groundwater quality assessment in the region of potential pollution sources can be performed through the use of index-based methods. The aim of this paper was to present the results of the groundwater quality assessment in the region of the zinc smelter in Miasteczko Śląskie (southern Poland) for the Quaternary aquifer based on monitoring data from 2000, 2011, and 2022. The following parameters were used in the analysis: Pb, Cd, Ni, Cu, Fe, Mn, and Zn. Three indices were calculated, i.e., the landfill water pollution index (LWPI), heavy metal pollution index (HPI), and metal index (MI). The values of the indicators suggest that in the described study area, there are waters that are under the strong influence of the zinc smelter infrastructure and landfills. The highest values obtained are about 17 for LWPI, about 66 for HPI, and about 133 for MI. These values indicate significant anthropogenic pollution of the groundwater of the Quaternary aquifer in the study area. Taking into account the values obtained for all three indices, it can be concluded that the HPI indicator is the least reliable due to the need to select two limit values (background and ideal content in waters for each of the parameters), which would suggest that in some cases, waters are not very contaminated. The other two indices show similarities (mainly in their spatial distribution), and only the choice of parameters determines which of the indices should be used. A comparison of the results of local groundwater quality monitoring with the results of the calculated indices indicate that the values of the calculated MI indices are closest to the actual water quality status.