Isotopic composition analysis contributes significantly to the investigation of the biogeochemical cycle of zinc with its economical, environmental and health implications. Interpretation of isotopic measurements is however hindered by the lack of a set of equilibrium isotopic fractionation factors between Zn-bearing minerals. In this study, equilibrium mass-dependent Zn isotope fractionation factors in Zn-bearing minerals are determined from first-principles calculations within the density functional theory (DFT) scheme. A wide range of minerals belonging to sulfide, carbonate, oxide, silicate, sulfate and arsenate mineral groups are modelled to account for the natural diversity of Zn crystal-chemical environment. Calculated reduced partition function ratios (β-factors) span a range smaller than 2‰ at 22 °C. All studied secondary minerals (adamite, gahnite, gunningite, hemimorphite, hydrozincite, zincite) but zinc carbonate (smithsonite) are isotopically heavier than zinc sulfide minerals (sphalerite and wurtzite) from which they could form through supergene processes. Zinc-aluminium spinel and zinc silicate are the isotopically heaviest minerals. The investigation of the crystal-chemical parameters at the origin of differences in isotopic properties shows an excellent linear correlation between ln β and Zn interatomic force constants. β-factors are also observed to increase when the Zn-first neighbour bond lengths decrease and charges on atoms involved in the bonding increase and vice versa. These findings are in line with the observation of heavy isotope enrichment in systems having the largest bond strength.