The heaviest iron-peak element Zinc (Zn) has been used as an important tracer of cosmic chemical evolution. Spectroscopic observations of the metal-poor stars in Local Group galaxies show an increasing trend of [Zn/Fe] ratios toward lower metallicity. However, the enrichment of Zn in galaxies is not well understood due to poor knowledge of astrophysical sites of Zn, as well as metal mixing in galaxies. Here we show possible explanations for the observed trend by taking into account electron-capture supernovae (ECSNe) as one of the sources of Zn in our chemodynamical simulations of dwarf galaxies. We find that the ejecta from ECSNe contribute to stars with [Zn/Fe]>~0.5. We also find that scatters of [Zn/Fe] in higher metallicities originate from the ejecta of type Ia supernovae. On the other hand, it appears difficult to explain the observed trends if we do not consider ECSNe as a source of Zn. These results come from an inhomogeneous spatial metallicity distribution due to the inefficiency of the metal mixing. We find that the optimal value of the scaling factor for the metal diffusion coefficient is ~0.01 in the shear- based metal mixing model in smoothed particle hydrodynamics simulations. These results suggest that ECSNe could be one of the contributors of the enrichment of Zn in galaxies.