Soil fungi are significantly resistant to heavy metals, which allows them to be used in biotechnologies for environmental bioremediation. In order to clarify the prospects for using the fungi in Zn-detoxifying technologies, we investigated in vitro the effect of fungal metabolism on Zn minerals formation. The cultivation of fungi with different acid-producing activities (Aspergillus niger and Penicillium chrysogenum) was carried out in a liquid Czapek–Dox nutrient medium with Zn concentrations from 250 to 2000 µmol within 28 days. The quantitates of low-molecular-weight organic acids, phosphates, and hydrophosphates ions in the medium were determined through chromatography–mass spectrometry; analysis of biomineralization products was carried out through powder X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. It was found that Zn in concentrations 250–500 μmol acts as a physiologically essential element, activating the growth of fungal mycelium, while at high concentrations (1000–2000 μmol), Zn acts as a toxic heavy metal, inhibiting fungal growth. Zn also activates the formation of oxalic acid by both species of fungi. But A. niger strongly acidified the medium, while P. chrysogenum leaves the medium pH close to neutral or slightly alkaline. Oxalate and phosphate crystallization occur with the participation of both fungal species. The ratio of biogenic oxalates and phosphates is directly dependent on the acid-reducing capacity of fungi. The solid solutions of katsarosite–glushinskite of the isodimorphic series with the general formula (Zn,Mg)C2O4·2H2O (Mg ions comes from Czapek–Dox medium) were detected at all Zn concentrations in a wide range of pH (from 2 to 9.0). The transition from monoclinic (α-modifications) to orthorhombic (β-modifications) occurs at the ratio Mg/Zn > 1. Fungal zinc phosphate hopeite Zn3(PO4)2·4H2O was formed at a near-neutral pH at high Zn concentrations (1000 and 2000 µmol/L). In the Zn example, it was shown that not only oxalate but also phosphate fungal biomineralization can be used for the environment detoxification of heavy metals. The application of phosphate biomineralization seems promising in the case of severe pollutions. To create a near-neutral medium favorable for the formation of phosphates, it is advisable to use soil fungi non-producing or weakly producing organic acids (for example, P. chrysogenum).