Novel dense and supported (polyacrylonitrile substrate) mixed matrix membranes based on biopolymer sodium alginate (SA), modified by Zr-MOFs were developed to improve pervaporation dehydration properties of a parent SA membrane. The following Zr-MOFs were synthesized and tested as modifiers: unmodified UiO-66 and modified UiO-66(NH₂)-AcOH and UiO-66(NH₂)-EDTA. Two kinds of mixed matrix membranes were developed: without additional treatment and cross-linked with calcium chloride. The synthesized Zr-MOFs nanoparticles and developed SA and SA-Zr-MOFs membranes were studied using Fourier-transform infrared spectroscopy, nuclear magnetic resonance, scanning electron microscopy, surface area measurement, atomic force microscopy, X-ray diffraction analysis, thermogravimetric analysis, and swelling experiments. Dense and supported membranes were tested for their transport properties in the pervaporation dehydration of isopropanol (12, 30 wt% water for the untreated membranes and 12–100 wt% water for the cross-linked membranes). The best transport properties (dehydration of water/isopropanol mixtures at 22 °C) were demonstrated by a supported cross-linked membrane, containing 15 wt% of UiO-66: permeation flux 0.47–3.38 kg/(m²h), water content in permeate 99.9-97.5 wt%.