Poly(phenylene isophthalamide) (PA) membranes modified with detonation nanodiamond (ND) particles have been prepared by solid-phase dispersion of powders of the components. The transport properties of dense film membranes containing up to 5 wt % ND have been studied in the methanol and methyl acetate mass transfer processes using the sorption and pervaporation methods. It has been shown that the sorption-diffusion characteristics of the membranes are improved owing to the incorporation of ND particles in the PA matrix. The experimental data on the pervaporation of a methanol-methyl acetate mixture have been used to calculate the classical parameters flux and separation factor and determine permeability and selectivity, characteristic driving force-normalized properties of the test membrane-penetrant system. The highest flux and separation factor values have been obtained for a membrane containing 3 wt % ND. It has been found that the characteristic properties of the membrane-penetrant system facilitate selective mass transport of a methanol-methyl acetate mixture using PA/ND membranes.