The physicochemical properties of soil and the unsaturated zone can have a large influence on the infiltration of precipitation into an aquifer. Soil permeability presents soil property that can be very variable. The main objectives of this study were to estimate differences in soil permeability in two dominant types of soils—Fluvisols and Eutric Cambisols—in the area of the Zagreb aquifer and determine the relationship between the physicochemical properties and the permeability of the analyzed soils. For this purpose, the particle size distribution, soil water retention curves (SWRCs), hydraulic parameters, and chemical properties of soils (i.e., electrical conductivity (EC), pH, carbonate content, cation exchange capacity (CEC), and total concentration of zinc (Zn)) from six soil profiles were observed. In general, the results show that Fluvisols have a smaller amount of clay and a higher amount of sand. Furthermore, particle size distribution indicates that Eutric Cambisols have smaller permeability and a slightly higher capacity for retention. In Eutric Cambisols, the percentages of clay, silt, and sand generally do not change with depth. On average, Fluvisols and Eutric Cambisols become impermeable when they reach different values of water content and effective saturation. All results suggest that Fluvisols generally have to desaturate more than Eutric Cambisols to become impermeable. The proportions of sand and Ks increases through the depth of all analyzed soils, while CEC, EC, and Zn decrease. The total Zn generally decrease with depth, which can be attributed to the aerodeposition in the surface horizons of the analyzed soils and their higher availability for binding/sorption elements. Generally, it can be seen that most Zn concentrations increase until 80 cm in depth, after which they decrease. This result indicates that, in these specific locations, the groundwater body is not under the influence of a potentially toxic metal, in this case Zn. Statistical analysis shows a strong correlation between Zn concentrations and some soil properties, such as soil texture and CEC. This may point to the prevalence of Zn retention. Furthermore, statistical results show that silt has a higher influence on the permeability of Eutric Cambisols than Fluvisols.